A new proposed Field primitive

💡 Ideas
1

I would like to propose a Field primitive to the current standard. A Field primitive would behave as described


Field([key,value],[ijk:i-infix j-prefix(default) k-postfix] [,toStringFormatter_callback()])

var add = new Field('op','+','i')
add.is() // "[ ] op:+ [ ]" //

var addTwo = new Field('op','+','i')
addTwo.is() // "[ ] op:+ [ ]" //

add == addTwo // false //

var num1 = new Field('int','1')
var num2 = new Field('int','2')
var num4 = new Field('int','4')

var numOnePlusNumOne = add.has(num1,num1)
numOnePlusNumOne.is() // "[ int:1 ] op:+ [ int:1 ]" //

var two = num2.has(numOnePlusNumOne)
two.is() // "int:2 [ [ int:1 ] op:+ [ int:1 ] ]" //

var strict_four = add.has(two)
strict_four = add.has(strict_four)

var four = add.has(two,two)
four.is() // "int:4 [ int:2 [ [ int:1 ] op:+ [ int:1 ] ] op:+ int:2 [ [ int:1 ] op:+ [ int:1 ] ] ]" //

four.superset("int:5") // "" //
four.superset("int:4") // "_" //
four.superset("int:2 op:+ int:2") // "int:4" //
four.superset("[ int:2 ] op:+ [ int:2 ]") // "int:4" //
four.superset("[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ int:2 ]") // "[ int:2 ] op:+ [ int:2 ]" //
four.superset("[ int:2 ] op:+ [ [ int:1 ] op:+ [ int:1 ] ] ") // "[ int:2 ] op:+ [ int:2 ]" //
four.superset("[ int:1 ] op:+ [ int:2 ]") // "" //

four.subset("int:5") // "" //
four.subset("int:4") // "[ int:2 ] op:+ [ int:2 ]" //
four.subset("[ int:2 ] op:+ [ int:2 ]") // "[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ [ int:1 ] op:+ [ int:1 ] ]" //
four.subset("[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ [ int:1 ] op:+ [ int:1 ] ]") // "_" //

strict_four.is() // "int:4 [ int:2 [ [ int:1 ] op:+ [ int:1 ] ] op:+ int:2 [ [ int:1 ] op:+ [ int:1 ] ] ]" //
strict_four.superset("[ int:2 ] op:+ [ [ int:1 ] op:+ [ int:1 ] ] ") // "[ int:2 ] op:+ [ int:2 ]" //
strict_four.superset("[ [ int:1 ] op:+ [ int:2 ] op:+ [ int:1 ] ] ") // "" //

var minus = new Field('op','-','i')
var one = minus.has([num2,num1])
one.superset("[ int:2 ] op:- [ int:1 ]") // "int:1" //
one.superset("[ int:1 ] op:- [ int:2 ]") // "" //
1 Like
2

Can you elaborate more on what this would do? Why the name “field”?

This seems like it’s an entirely new DSL - is this based on anything in common usage?

3

Q: A new DSL ? I'm not aware of the term. Does it preserve representation? You may call them "Fields", or a "Set", or flat "Network" -- so long as the lexical structure (key/value pairs) and semantics (hierchial structure) is preserved for optimal search performance.
My goal is optimal search perfomance across groups of Fields or Sets (eg the largest number of odd primes less than R in the rational number field Q; or the number of optimal traveling-salesman routes in a 100-mile region, bounded by time metric Q; or the highest BETA stocks having PE ratios greater than P, during a given time-period T; or the largest group of AUGUC RNA codons in a genome for biomedical research...etc ), again the goal is to derive meaningful correlation

  int
---------------------------------------------------------------
  4                                                           |
                                                              |
     op                                                       |
     -------------------------------------------------        |
     |    +                                          |        |
     |                                               |        |
     |    int                                        |        |
     |     -----------------------------------       |        |
     |     |    2                            |       |        |
     |     |                                 |       |        |
     |     |        op                       |       |        |
     |     |        --------------------     |       |        |
     |     |        |   +              |     |       |        |
     |     |        |                  |     |       |        |
     |     |        |   int     int    |     |       |        |
     |     |        |   -----   -----  |     |       |        |
     |     |        |   [ 1 ]   [ 1 ]  |     |       |        |
     |     |        |   -----   -----  |     |       |        |
     |     |        |                  |     |       |        |
     |     |        --------------------     |       |        |
     |     |                                 |       |        |
     |     ----------------------------------        |        |
     |                                               |        |
     |    int                                        |        |
     |     -----------------------------------       |        |
     |     |    2                            |       |        |
     |     |                                 |       |        |
     |     |        op                       |       |        |
     |     |        --------------------     |       |        |
     |     |        |   +              |     |       |        |
     |     |        |                  |     |       |        |
     |     |        |   int     int    |     |       |        |
     |     |        |   -----   -----  |     |       |        |
     |     |        |   [ 1 ]   [ 1 ]  |     |       |        |
     |     |        |   -----   -----  |     |       |        |
     |     |        |                  |     |       |        |
     |     |        --------------------     |       |        |
     |     |                                 |       |        |
     |     ----------------------------------        |        |
     |                                               |        |
     |                                               |        |
     -------------------------------------------------        |
                                                              |
                                                              |
---------------------------------------------------------------
4

Oh, you're talking about fields not about fields.

But still, please elaborate why you think this needs to become a new primitive in the language. It seems like the problems to be solved with this could also be solved by a userspace library. Also the use case is quite specific, how would the average web programmer benefit from this?

5

I imagine Field entities as idealized Sets with improved data-tagging features and optimal search performance:

I agree with your earlier statement. Algorithms, in general are more powerful, yes -- but nothing can best discrete data structures, in terms of their ease of data-manipulation, conversion and search performance.

Field([[value],...],[ijkldmrsy] [,toStringFormatter_callback()])

FLAGS

i-infix
j-prefix (default)
k-postfix
d-multiple-delimited
s-single-delimiter (default)
m-mesh-topology a-b a-c b-c b-d
l-line-topology (default) a-b-c-d
r-ring-topology a-b-c-d-a
y-fully-connected-topology a-[-bcd] b-[-acd] c-[-abd] d-[-abc]

Note: flags "j" and "i" are default sugars for "jls" and "ils", respectively -- unless stated otherwise.

EXAMPLES

let NumberField = new Field([{ Ring:z }])[0]
let n1 = new Field([{ int:1 }])[0]
let n2 = new Field([{ int:2 }])[0]
let n3 = new Field([{ int:3 }])[0]
let n4 = new Field([{ int:4 }])[0]

let FieldA = NumberField.eq([ n1,n2,n3,n4 ])[0]
let FieldB = NumberField.eq([ n1,n2,n3 ])[0]
let FieldC = NumberField.eq([ n3,n2,n1 ])[0]
let FieldD = NumberField.eq([ n3,n2,n1 ],'ily')[0]
let FieldE = FieldC

FieldA.has(n1) && FieldA.has(n2) && FieldA.has(n3) // true
FieldA.has(FieldB) // true
FieldA.has(FieldC) // false !
FieldA.has(FieldD) // true
FieldC == FieldD // false
FieldC == FieldE // false !

FieldA.is() // "Ring:Z [ int:1 int:2 int:3 int:4 ]"
FieldB.is() // "Ring:Z [ int:1 int:2 int:3 ]"
FieldC.is() // "Ring:Z [ int:3 int:2 int:1 ]"
FieldD.is() // "Ring:Z [ int:3 int:2 int:1 ]y"

// (FieldB in FieldA) == true //
FieldA.superset(FieldB.is()) // "Ring:Z [ int:1 int:2 int:3 int:4 ]"

// (FieldB.is() in FieldA.is()) == false, FieldA was created using a single statement and thus is "irreducible"
FieldA.subset(FieldB.is()) // ""


let add = new Field([{ op:'+' }], 'i')[0]
add.is() // "[ ] op:+ [ ]"

let addTwo = new Field([{ op:'+' }], 'i')[0]
addTwo.is() // "[ ] op:+ [ ]"

add == addTwo // false

let num1 = new Field([{ int:1 }])[0]
let num2 = new Field([{ int:2 }])[0]
let num4 = new Field([{ int:4 }])[0]

let numOnePlusNumOne = add.eq(num1,num1)
numOnePlusNumOne.is() // "[ int:1 ] op:+ [ int:1 ]"

let two = num2.eq(numOnePlusNumOne)
two.is() // "int:2 [ [ int:1 ] op:+ [ int:1 ] ]"

let strict_four = add.eq(two)
strict_four = add.eq(strict_four)

let four = add.eq(two,two)
four.is() // "int:4 [ int:2 [ [ int:1 ] op:+ [ int:1 ] ] op:+ int:2 [ [ int:1 ] op:+ [ int:1 ] ] ]"

four.superset("int:5") // ""
four.superset("int:4") // "_"
four.superset("int:2 op:+ int:2") // "int:4"
four.superset("[ int:2 ] op:+ [ int:2 ]") // "int:4"
four.superset("[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ int:2 ]") // "[ int:2 ] op:+ [ int:2 ]"
four.superset("[ int:2 ] op:+ [ [ int:1 ] op:+ [ int:1 ] ] ") // "[ int:2 ] op:+ [ int:2 ]"
four.superset("[ int:1 ] op:+ [ int:2 ]") // ""

four.subset("int:5") // ""
four.subset("int:4") // "[ int:2 ] op:+ [ int:2 ]"
four.subset("[ int:2 ] op:+ [ int:2 ]") // "[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ [ int:1 ] op:+ [ int:1 ] ]"
four.subset("[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ [ int:1 ] op:+ [ int:1 ] ]") // "_"

strict_four.is() // "int:4 [ int:2 [ [ int:1 ] op:+ [ int:1 ] ] op:+ int:2 [ [ int:1 ] op:+ [ int:1 ] ] ]"
strict_four.superset("[ int:2 ] op:+ [ [ int:1 ] op:+ [ int:1 ] ] ") // "[ int:2 ] op:+ [ int:2 ]"
strict_four.superset("[ [ int:1 ] op:+ [ int:2 ] op:+ [ int:1 ] ] ") // ""

let minus = new Field([{ op:'-' }],'i')[0]
let one = minus.eq([ [num2,num1] ])
one.superset("[ int:2 ] op:- [ int:1 ]") // "int:1"
one.superset("[ int:1 ] op:- [ int:2 ]") // ""
6

Another trivial example

let genus = new Field([{ genus:'malus' }])[0]
let apple = new Field([{ noun:'apple' }])[0]
let synon1 = new Field([{ synonym:'pink pearl' }])[0]
let synon2 = new Field([{ synonym:'ambrosia' }])[0]
let synon3 = new Field([{ synonym:'arkansas black' }])[0]
let synon4 = new Field([{ synonym:'wine sap' }])[0]
let synon5 = new Field([{ synonym:'opal' }])[0]

let fruit = genus.eq([apple,synon1,synon2,synon3,synon4,synon5], 'ily')
fruit.has( apple ) // true
fruit.is() // "genus:malus [ noun:apple synonym:'pink pearl' synonym:'ambrosia' synonym:'arkansas black' synonym:'wine sap' synonym:'opal' ]y"
7

Or perhaps instead of "superset/subset" properties, a Field could have "layers"

fruit.layer( 0 ).is() // "genus:malus [ noun:apple synonym:'pink pearl' synonym:'ambrosia' synonym:'arkansas black' synonym:'wine sap' synonym:'opal' ]y"
four.layerBelow(twoPlusTwo.is()) "[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ [ int:1 ] op:+ [ int:1 ] ]"
four.layerAbove(twoPlusTwo.is()) "int:4"
four.layerAt( ... )
8

Can we devise a novel data-structure to emulate this ?

9

Or perhaps allow Field.has( ... ) to return an index iff true, else -1

fruit.layer( 0 ).is() // "genus:malus [ noun:apple synonym:'pink pearl' synonym:'ambrosia' synonym:'arkansas black' synonym:'wine sap' synonym:'opal' ]y"
// let nextLayer ?= four.has(twoPlusTwo) + 1 : -1 ;
// let lastLayer ?= four.has(twoPlusTwo) - 1 : -1 ;
let nextLayer = four.has( twoPlusTwo ) + 1 ;
let lastLayer = four.has( twoPlusTwo ) - 1 ;
four.layer( nextLayer ).is() // "int:4"
four.layer( lastLayer ).is() // "[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ [ int:1 ] op:+ [ int:1 ] ]"
10

Thus

Field([[value],...],[ijkldmrsy] [,toStringFormatter_callback()])

FLAGS

i-infix
j-prefix (default)
k-postfix
d-multiple-delimited
s-single-delimiter (default)
m-mesh-topology a-b a-c b-c b-d
l-line-topology (default) a-b-c-d
r-ring-topology a-b-c-d-a
y-fully-connected-topology a-[bcd] b-[acd] c-[abd] d-[abc]

Note: flags "j" and "i" are default sugars for "jls" and "ils", respectively -- unless stated otherwise.

EXAMPLES

let NumberField = new Field([{ Ring:z }])[0]
let n1 = new Field([{ int:1 }])[0]
let n2 = new Field([{ int:2 }])[0]
let n3 = new Field([{ int:3 }])[0]
let n4 = new Field([{ int:4 }])[0]

let FieldA = NumberField.eq([ n1,n2,n3,n4 ])[0]
let FieldB = NumberField.eq([ n1,n2,n3 ])[0]
let FieldC = NumberField.eq([ n3,n2,n1 ])[0]
let FieldD = NumberField.eq([ n3,n2,n1 ],'ily')[0]
let FieldE = FieldC

FieldA.has( n1 ) && FieldA.has( n2 ) && FieldA.has( n3 ) // true
FieldA.has( FieldB ) // 0 (index)
FieldA.has( FieldC ) // -1
FieldA.has( FieldD ) // 0 (index)
FieldB.has( FieldD ) // -1
FieldC.has( FieldD ) // 0 (index)
FieldD.has( FieldC ) // 0 (index)
FieldD.has( FieldB ) // 0 (index)
FieldC == FieldD // false
FieldC == FieldE // false

FieldA.is() // "Ring:Z [ int:1 int:2 int:3 int:4 ]"
FieldB.is() // "Ring:Z [ int:1 int:2 int:3 ]"
FieldC.is() // "Ring:Z [ int:3 int:2 int:1 ]"
FieldD.is() // "Ring:Z [ int:3 int:2 int:1 ]y"

// (FieldB in FieldA) == true //
FieldA.layer( FieldA.has( FieldB ) ).is() // "Ring:Z [ int:1 int:2 int:3 int:4 ]"

// FieldA has no descendant and thus is "irreducible"
FieldA.layer( FieldA.has( FieldB ) - 1 ).is() // ""


let add = new Field([{ op:'+' }], 'i')[0]
add.is() // "[ ] op:+ [ ]"

let addTwo = new Field([{ op:'+' }], 'i')[0]
addTwo.is() // "[ ] op:+ [ ]"

add == addTwo // false

let num1 = new Field([{ int:1 }])[0]
let num2 = new Field([{ int:2 }])[0]
let num4 = new Field([{ int:4 }])[0]

let numOnePlusNumOne = add.eq([ num1,num1 ])[0]
numOnePlusNumOne.is() // "[ int:1 ] op:+ [ int:1 ]"

let two = num2.eq([ numOnePlusNumOne ])[0]
two.is() // "int:2 [ [ int:1 ] op:+ [ int:1 ] ]"

let twoPlusTwo = add.eq([ two,two ])[0]
twoPlusTwo.is() // [ int:2 [ [ int:1 ] op:+ [ int:1 ] ] op:+ int:2 [ [ int:1 ] op:+ [ int:1 ] ] ]

let four = num4.eq([ twoPlusTwo ])[0]
four.is() // "int:4 [ int:2 [ [ int:1 ] op:+ [ int:1 ] ] op:+ int:2 [ [ int:1 ] op:+ [ int:1 ] ] ]"

four.layer( four.has( five ) ).is() // ""
four.layer( four.has( four ) + 1 ).is() // "_"
four.layer( four.has( twoPlusTwo ) ).is() // "int:4"
four.layer( four.has( onePlusOnePlusTwo ) + 1 ).is() // "[ int:2 ] op:+ [ int:2 ]"
four.layer( four.has( twoPlusOnePlusOne ) + 1 ).is() // "[ int:2 ] op:+ [ int:2 ]"
four.layer( four.has( OnePlusTwo ) ).is() // ""

four.layer( four.has( five ) - 1 ).is() // ""
four.layer( four.has( four ) ).is() // "_"
four.layer( four.has( twoPlusTwo ) - 1 ).is() // "[ [ int:1 ] op:+ [ int:1 ] ] op:+ [ [ int:1 ] op:+ [ int:1 ] ]"
four.layer( four.has( onePlusOnePlusOnePlusOne ) - 1 ).is() // "_"

let strict_two = add.eq([ two ])[0]
let strict_twoPlusTwo = add.eq([ strict_two ])[0]
let strict_four = num4.eq([ strict_twoPlusTwo ])[0]
strict_four.is() // "int:4 [ [ [  ] op:+ [ int:2 [  [ int:1 op:+ int:1 ] op:+ [ int:1 op:+ int:1 ] ] ] ] op:+ [ [  ] op:+ [ int:2 [  [ int:1 op:+ int:1 ] op:+ [ int:1 op:+ int:1 ] ] ] ] ]"

strict_four.layer( strict_four.has( twoPlusOnePlusOne ) + 1 ).is() // "[ int:2 ] op:+ [ int:2 ]"
strict_four.layer( strict_four.has( onePlusTwoPlusOne ) + 1 ).is() // ""

let minus = new Field([{ op:'-' }],'i')[0]
let twoMinusOne = minus.eq([ num2,num1 ])

let one = num1.eq([ twoMinusOne ])[0]
one.is() // "int:1 [ int:2 op:- int:1 ]"
one.layer( one.has( twoMinusOne ) + 1 ).is() // "int:1"
one.layer( one.has( oneMinusTwo ) ).is() // ""
11

What precisely is the concrete use case here?

12

My current interests are in the examples, above.

Thanks

I desire a Field entity or enhanced Set which preserves the lexical structure as well as the designated hierarchical structure ie its "topology" of inserted items and their key/value pairs .

A "flat" network, which enhances search performance across these Sets or Fields .

13

Current applicable disciplines are : Economics, Computer Science, Mathematics
Current applicable areas are : Automated Theorem Proving (ATP), Interactive Theorem Proving (ITP), Macro economics, Investment Banking, Accounting/Auditing, Market Data Compliance , Machine Learning, Deep Learning, A.I., Natural Language Inferencing, Logic, Algebraic Number Theory, Graph Theory, Combinatorics

14

That's abstract, not concrete. What precise problems does this simplify solving? In particular, for each of those applicable areas you listed, can you give an example of such a use case?

1 Like
15

Ok . I'll need about 2 days

16 
Given axioms

1 + 1 = 2
1 + 2 = 3
2 + 2 = 4
1 + 4 = 5
3 + 3 = 6
1 + 6 = 7
4 + 4 = 8
1 + 8 = 9
5 + 5 = 10
1 + 10 = 11
6 + 6 = 12
1 + 12 = 13
7 + 7 = 14
1 + 14 = 15
8 + 8 = 16
1 + 16 = 17
9 + 9 = 18
1 + 18 = 19
10 + 10 = 20
1 + 20 = 21
11 + 11 = 22
1 + 22 = 23
12 + 12 = 24
1 + 24 = 25
13 + 13 = 26
1 + 26 = 27
14 + 14 = 28
1 + 28 = 29
15 + 15 = 30
1 + 30 = 31
16 + 16 = 32
1 + 32 = 33
17 + 17 = 34
1 + 34 = 35
18 + 18 = 36
1 + 36 = 37
19 + 19 = 38
1 + 38 = 39
20 + 20 = 40
1 + 40 = 41
21 + 21 = 42
1 + 42 = 43
22 + 22 = 44
1 + 44 = 45
23 + 23 = 46
1 + 46 = 47
24 + 24 = 48
1 + 48 = 49
25 + 25 = 50
1 + 50 = 51
26 + 26 = 52
1 + 52 = 53
27 + 27 = 54
1 + 54 = 55
28 + 28 = 56
1 + 56 = 57
29 + 29 = 58
1 + 58 = 59
30 + 30 = 60
1 + 60 = 61
31 + 31 = 62
1 + 62 = 63
32 + 32 = 64
1 + 64 = 65
33 + 33 = 66
1 + 66 = 67
34 + 34 = 68
1 + 68 = 69
35 + 35 = 70
1 + 70 = 71
36 + 36 = 72
1 + 72 = 73
37 + 37 = 74
1 + 74 = 75
38 + 38 = 76
1 + 76 = 77
39 + 39 = 78
1 + 78 = 79
40 + 40 = 80
1 + 80 = 81
41 + 41 = 82
1 + 82 = 83
42 + 42 = 84
1 + 84 = 85
43 + 43 = 86
1 + 86 = 87
44 + 44 = 88
1 + 88 = 89
45 + 45 = 90
1 + 90 = 91
46 + 46 = 92
1 + 92 = 93
47 + 47 = 94
1 + 94 = 95
48 + 48 = 96
1 + 96 = 97
49 + 49 = 98
1 + 98 = 99
50 + 50 = 100
1 + 100 = 101
51 + 51 = 102
1 + 102 = 103
52 + 52 = 104
1 + 104 = 105
53 + 53 = 106
1 + 106 = 107
54 + 54 = 108
1 + 108 = 109
55 + 55 = 110
1 + 110 = 111
56 + 56 = 112
1 + 112 = 113
57 + 57 = 114
1 + 114 = 115
58 + 58 = 116
1 + 116 = 117
59 + 59 = 118
1 + 118 = 119
60 + 60 = 120
1 + 120 = 121
61 + 61 = 122
1 + 122 = 123
62 + 62 = 124
1 + 124 = 125
63 + 63 = 126
1 + 126 = 127
64 + 64 = 128
1 + 128 = 129
65 + 65 = 130
1 + 130 = 131
66 + 66 = 132
1 + 132 = 133
67 + 67 = 134
1 + 134 = 135
68 + 68 = 136
1 + 136 = 137
69 + 69 = 138
1 + 138 = 139
70 + 70 = 140
1 + 140 = 141
71 + 71 = 142
1 + 142 = 143
72 + 72 = 144
1 + 144 = 145
73 + 73 = 146
1 + 146 = 147
74 + 74 = 148
1 + 148 = 149
75 + 75 = 150
1 + 150 = 151
76 + 76 = 152
1 + 152 = 153
77 + 77 = 154
1 + 154 = 155
78 + 78 = 156
1 + 156 = 157
79 + 79 = 158
1 + 158 = 159
80 + 80 = 160
1 + 160 = 161
81 + 81 = 162
1 + 162 = 163
82 + 82 = 164
1 + 164 = 165
83 + 83 = 166
1 + 166 = 167
84 + 84 = 168
1 + 168 = 169
85 + 85 = 170
1 + 170 = 171
86 + 86 = 172
1 + 172 = 173
87 + 87 = 174
1 + 174 = 175
88 + 88 = 176
1 + 176 = 177
89 + 89 = 178
1 + 178 = 179
90 + 90 = 180
1 + 180 = 181
91 + 91 = 182
1 + 182 = 183
92 + 92 = 184
1 + 184 = 185
93 + 93 = 186
1 + 186 = 187
94 + 94 = 188
1 + 188 = 189
95 + 95 = 190
1 + 190 = 191
96 + 96 = 192
1 + 192 = 193
97 + 97 = 194
1 + 194 = 195
98 + 98 = 196
1 + 196 = 197
99 + 99 = 198
1 + 198 = 199
100 + 100 = 200
1 + 200 = 201
101 + 101 = 202
1 + 202 = 203
102 + 102 = 204
1 + 204 = 205
103 + 103 = 206
1 + 206 = 207
104 + 104 = 208
1 + 208 = 209
105 + 105 = 210
1 + 210 = 211
106 + 106 = 212
1 + 212 = 213
107 + 107 = 214
1 + 214 = 215
108 + 108 = 216
1 + 216 = 217
109 + 109 = 218
1 + 218 = 219
110 + 110 = 220
1 + 220 = 221
111 + 111 = 222
1 + 222 = 223
112 + 112 = 224
1 + 224 = 225
113 + 113 = 226
1 + 226 = 227
114 + 114 = 228
1 + 228 = 229
115 + 115 = 230
1 + 230 = 231
116 + 116 = 232
1 + 232 = 233
117 + 117 = 234
1 + 234 = 235
118 + 118 = 236
1 + 236 = 237
119 + 119 = 238
1 + 238 = 239
120 + 120 = 240
1 + 240 = 241
121 + 121 = 242
1 + 242 = 243
122 + 122 = 244
1 + 244 = 245
123 + 123 = 246
17 
Prove 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 246
18 
let add = new Field([ { op:'+' } ],'i')[0]

let int1 = new Field([ { int:1 } ])[0]
let int2 = new Field([ { int:2 } ])[0]
let int3 = new Field([ { int:3 } ])[0]
let int4 = new Field([ { int:4 } ])[0]
let int5 = new Field([ { int:5 } ])[0]
let int6 = new Field([ { int:6 } ])[0]
let int7 = new Field([ { int:7 } ])[0]
let int8 = new Field([ { int:8 } ])[0]
let int9 = new Field([ { int:9 } ])[0]
let int10 = new Field([ { int:10 } ])[0]
let int11 = new Field([ { int:11 } ])[0]
let int12 = new Field([ { int:12 } ])[0]
let int13 = new Field([ { int:13 } ])[0]
let int14 = new Field([ { int:14 } ])[0]
let int15 = new Field([ { int:15 } ])[0]
let int16 = new Field([ { int:16 } ])[0]
let int17 = new Field([ { int:17 } ])[0]
let int18 = new Field([ { int:18 } ])[0]
let int19 = new Field([ { int:19 } ])[0]
let int20 = new Field([ { int:20 } ])[0]
let int21 = new Field([ { int:21 } ])[0]
let int22 = new Field([ { int:22 } ])[0]
let int23 = new Field([ { int:23 } ])[0]
let int24 = new Field([ { int:24 } ])[0]
let int25 = new Field([ { int:25 } ])[0]
let int26 = new Field([ { int:26 } ])[0]
let int27 = new Field([ { int:27 } ])[0]
let int28 = new Field([ { int:28 } ])[0]
let int29 = new Field([ { int:29 } ])[0]
let int30 = new Field([ { int:30 } ])[0]
let int31 = new Field([ { int:31 } ])[0]
let int32 = new Field([ { int:32 } ])[0]
let int33 = new Field([ { int:33 } ])[0]
let int34 = new Field([ { int:34 } ])[0]
let int35 = new Field([ { int:35 } ])[0]
let int36 = new Field([ { int:36 } ])[0]
let int37 = new Field([ { int:37 } ])[0]
let int38 = new Field([ { int:38 } ])[0]
let int39 = new Field([ { int:39 } ])[0]
let int40 = new Field([ { int:40 } ])[0]
let int41 = new Field([ { int:41 } ])[0]
let int42 = new Field([ { int:42 } ])[0]
let int43 = new Field([ { int:43 } ])[0]
let int44 = new Field([ { int:44 } ])[0]
let int45 = new Field([ { int:45 } ])[0]
let int46 = new Field([ { int:46 } ])[0]
let int47 = new Field([ { int:47 } ])[0]
let int48 = new Field([ { int:48 } ])[0]
let int49 = new Field([ { int:49 } ])[0]
let int50 = new Field([ { int:50 } ])[0]
let int51 = new Field([ { int:51 } ])[0]
let int52 = new Field([ { int:52 } ])[0]
let int53 = new Field([ { int:53 } ])[0]
let int54 = new Field([ { int:54 } ])[0]
let int55 = new Field([ { int:55 } ])[0]
let int56 = new Field([ { int:56 } ])[0]
let int57 = new Field([ { int:57 } ])[0]
let int58 = new Field([ { int:58 } ])[0]
let int59 = new Field([ { int:59 } ])[0]
let int60 = new Field([ { int:60 } ])[0]
let int61 = new Field([ { int:61 } ])[0]
let int62 = new Field([ { int:62 } ])[0]
let int63 = new Field([ { int:63 } ])[0]
let int64 = new Field([ { int:64 } ])[0]
let int65 = new Field([ { int:65 } ])[0]
let int66 = new Field([ { int:66 } ])[0]
let int67 = new Field([ { int:67 } ])[0]
let int68 = new Field([ { int:68 } ])[0]
let int69 = new Field([ { int:69 } ])[0]
let int70 = new Field([ { int:70 } ])[0]
let int71 = new Field([ { int:71 } ])[0]
let int72 = new Field([ { int:72 } ])[0]
let int73 = new Field([ { int:73 } ])[0]
let int74 = new Field([ { int:74 } ])[0]
let int75 = new Field([ { int:75 } ])[0]
let int76 = new Field([ { int:76 } ])[0]
let int77 = new Field([ { int:77 } ])[0]
let int78 = new Field([ { int:78 } ])[0]
let int79 = new Field([ { int:79 } ])[0]
let int80 = new Field([ { int:80 } ])[0]
let int81 = new Field([ { int:81 } ])[0]
let int82 = new Field([ { int:82 } ])[0]
let int83 = new Field([ { int:83 } ])[0]
let int84 = new Field([ { int:84 } ])[0]
let int85 = new Field([ { int:85 } ])[0]
let int86 = new Field([ { int:86 } ])[0]
let int87 = new Field([ { int:87 } ])[0]
let int88 = new Field([ { int:88 } ])[0]
let int89 = new Field([ { int:89 } ])[0]
let int90 = new Field([ { int:90 } ])[0]
let int91 = new Field([ { int:91 } ])[0]
let int92 = new Field([ { int:92 } ])[0]
let int93 = new Field([ { int:93 } ])[0]
let int94 = new Field([ { int:94 } ])[0]
let int95 = new Field([ { int:95 } ])[0]
let int96 = new Field([ { int:96 } ])[0]
let int97 = new Field([ { int:97 } ])[0]
let int98 = new Field([ { int:98 } ])[0]
let int99 = new Field([ { int:99 } ])[0]
let int100 = new Field([ { int:100 } ])[0]
let int101 = new Field([ { int:101 } ])[0]
let int102 = new Field([ { int:102 } ])[0]
let int103 = new Field([ { int:103 } ])[0]
let int104 = new Field([ { int:104 } ])[0]
let int105 = new Field([ { int:105 } ])[0]
let int106 = new Field([ { int:106 } ])[0]
let int107 = new Field([ { int:107 } ])[0]
let int108 = new Field([ { int:108 } ])[0]
let int109 = new Field([ { int:109 } ])[0]
let int110 = new Field([ { int:110 } ])[0]
let int111 = new Field([ { int:111 } ])[0]
let int112 = new Field([ { int:112 } ])[0]
let int113 = new Field([ { int:113 } ])[0]
let int114 = new Field([ { int:114 } ])[0]
let int115 = new Field([ { int:115 } ])[0]
let int116 = new Field([ { int:116 } ])[0]
let int117 = new Field([ { int:117 } ])[0]
let int118 = new Field([ { int:118 } ])[0]
let int119 = new Field([ { int:119 } ])[0]
let int120 = new Field([ { int:120 } ])[0]
let int121 = new Field([ { int:121 } ])[0]
let int122 = new Field([ { int:122 } ])[0]
let int123 = new Field([ { int:123 } ])[0]
let int124 = new Field([ { int:124 } ])[0]
let int125 = new Field([ { int:125 } ])[0]
let int126 = new Field([ { int:126 } ])[0]
let int127 = new Field([ { int:127 } ])[0]
let int128 = new Field([ { int:128 } ])[0]
let int129 = new Field([ { int:129 } ])[0]
let int130 = new Field([ { int:130 } ])[0]
let int131 = new Field([ { int:131 } ])[0]
let int132 = new Field([ { int:132 } ])[0]
let int133 = new Field([ { int:133 } ])[0]
let int134 = new Field([ { int:134 } ])[0]
let int135 = new Field([ { int:135 } ])[0]
let int136 = new Field([ { int:136 } ])[0]
let int137 = new Field([ { int:137 } ])[0]
let int138 = new Field([ { int:138 } ])[0]
let int139 = new Field([ { int:139 } ])[0]
let int140 = new Field([ { int:140 } ])[0]
let int141 = new Field([ { int:141 } ])[0]
let int142 = new Field([ { int:142 } ])[0]
let int143 = new Field([ { int:143 } ])[0]
let int144 = new Field([ { int:144 } ])[0]
let int145 = new Field([ { int:145 } ])[0]
let int146 = new Field([ { int:146 } ])[0]
let int147 = new Field([ { int:147 } ])[0]
let int148 = new Field([ { int:148 } ])[0]
let int149 = new Field([ { int:149 } ])[0]
let int150 = new Field([ { int:150 } ])[0]
let int151 = new Field([ { int:151 } ])[0]
let int152 = new Field([ { int:152 } ])[0]
let int153 = new Field([ { int:153 } ])[0]
let int154 = new Field([ { int:154 } ])[0]
let int155 = new Field([ { int:155 } ])[0]
let int156 = new Field([ { int:156 } ])[0]
let int157 = new Field([ { int:157 } ])[0]
let int158 = new Field([ { int:158 } ])[0]
let int159 = new Field([ { int:159 } ])[0]
let int160 = new Field([ { int:160 } ])[0]
let int161 = new Field([ { int:161 } ])[0]
let int162 = new Field([ { int:162 } ])[0]
let int163 = new Field([ { int:163 } ])[0]
let int164 = new Field([ { int:164 } ])[0]
let int165 = new Field([ { int:165 } ])[0]
let int166 = new Field([ { int:166 } ])[0]
let int167 = new Field([ { int:167 } ])[0]
let int168 = new Field([ { int:168 } ])[0]
let int169 = new Field([ { int:169 } ])[0]
let int170 = new Field([ { int:170 } ])[0]
let int171 = new Field([ { int:171 } ])[0]
let int172 = new Field([ { int:172 } ])[0]
let int173 = new Field([ { int:173 } ])[0]
let int174 = new Field([ { int:174 } ])[0]
let int175 = new Field([ { int:175 } ])[0]
let int176 = new Field([ { int:176 } ])[0]
let int177 = new Field([ { int:177 } ])[0]
let int178 = new Field([ { int:178 } ])[0]
let int179 = new Field([ { int:179 } ])[0]
let int180 = new Field([ { int:180 } ])[0]
let int181 = new Field([ { int:181 } ])[0]
let int182 = new Field([ { int:182 } ])[0]
let int183 = new Field([ { int:183 } ])[0]
let int184 = new Field([ { int:184 } ])[0]
let int185 = new Field([ { int:185 } ])[0]
let int186 = new Field([ { int:186 } ])[0]
let int187 = new Field([ { int:187 } ])[0]
let int188 = new Field([ { int:188 } ])[0]
let int189 = new Field([ { int:189 } ])[0]
let int190 = new Field([ { int:190 } ])[0]
let int191 = new Field([ { int:191 } ])[0]
let int192 = new Field([ { int:192 } ])[0]
let int193 = new Field([ { int:193 } ])[0]
let int194 = new Field([ { int:194 } ])[0]
let int195 = new Field([ { int:195 } ])[0]
let int196 = new Field([ { int:196 } ])[0]
let int197 = new Field([ { int:197 } ])[0]
let int198 = new Field([ { int:198 } ])[0]
let int199 = new Field([ { int:199 } ])[0]
let int200 = new Field([ { int:200 } ])[0]
let int201 = new Field([ { int:201 } ])[0]
let int202 = new Field([ { int:202 } ])[0]
let int203 = new Field([ { int:203 } ])[0]
let int204 = new Field([ { int:204 } ])[0]
let int205 = new Field([ { int:205 } ])[0]
let int206 = new Field([ { int:206 } ])[0]
let int207 = new Field([ { int:207 } ])[0]
let int208 = new Field([ { int:208 } ])[0]
let int209 = new Field([ { int:209 } ])[0]
let int210 = new Field([ { int:210 } ])[0]
let int211 = new Field([ { int:211 } ])[0]
let int212 = new Field([ { int:212 } ])[0]
let int213 = new Field([ { int:213 } ])[0]
let int214 = new Field([ { int:214 } ])[0]
let int215 = new Field([ { int:215 } ])[0]
let int216 = new Field([ { int:216 } ])[0]
let int217 = new Field([ { int:217 } ])[0]
let int218 = new Field([ { int:218 } ])[0]
let int219 = new Field([ { int:219 } ])[0]
let int220 = new Field([ { int:220 } ])[0]
let int221 = new Field([ { int:221 } ])[0]
let int222 = new Field([ { int:222 } ])[0]
let int223 = new Field([ { int:223 } ])[0]
let int224 = new Field([ { int:224 } ])[0]
let int225 = new Field([ { int:225 } ])[0]
let int226 = new Field([ { int:226 } ])[0]
let int227 = new Field([ { int:227 } ])[0]
let int228 = new Field([ { int:228 } ])[0]
let int229 = new Field([ { int:229 } ])[0]
let int230 = new Field([ { int:230 } ])[0]
let int231 = new Field([ { int:231 } ])[0]
let int232 = new Field([ { int:232 } ])[0]
let int233 = new Field([ { int:233 } ])[0]
let int234 = new Field([ { int:234 } ])[0]
let int235 = new Field([ { int:235 } ])[0]
let int236 = new Field([ { int:236 } ])[0]
let int237 = new Field([ { int:237 } ])[0]
let int238 = new Field([ { int:238 } ])[0]
let int239 = new Field([ { int:239 } ])[0]
let int240 = new Field([ { int:240 } ])[0]
let int241 = new Field([ { int:241 } ])[0]
let int242 = new Field([ { int:242 } ])[0]
let int243 = new Field([ { int:243 } ])[0]
let int244 = new Field([ { int:244 } ])[0]
let int245 = new Field([ { int:245 } ])[0]
let int246 = new Field([ { int:246 } ])[0]
19 
// Axioms
let num1 = int1
let num2 = add.eq([ [int1,int1] ],'y')
let num3 = add.eq([ [int2,int1] ],'y')
let num4 = add.eq([ [int3,int1],[int2,int2] ],'y')
let num5 = add.eq([ [int4,int1],[int3,int2] ],'y')
let num6 = add.eq([ [int5,int1],[int4,int2],[int3,int3] ],'y')
let num7 = add.eq([ [int6,int1],[int5,int2],[int4,int3] ],'y')
let num8 = add.eq([ [int7,int1],[int6,int2],[int5,int3],[int4,int4] ],'y')
let num9 = add.eq([ [int8,int1],[int7,int2],[int6,int3],[int5,int4] ],'y')
let num10 = add.eq([ [int9,int1],[int8,int2],[int7,int3],[int6,int4],[int5,int5] ],'y')
let num11 = add.eq([ [int10,int1],[int9,int2],[int8,int3],[int7,int4],[int6,int5] ],'y')
let num12 = add.eq([ [int11,int1],[int10,int2],[int9,int3],[int8,int4],[int7,int5],[int6,int6] ],'y')
let num13 = add.eq([ [int12,int1],[int11,int2],[int10,int3],[int9,int4],[int8,int5],[int7,int6] ],'y')
let num14 = add.eq([ [int13,int1],[int12,int2],[int11,int3],[int10,int4],[int9,int5],[int8,int6],[int7,int7] ],'y')
let num15 = add.eq([ [int14,int1],[int13,int2],[int12,int3],[int11,int4],[int10,int5],[int9,int6],[int8,int7] ],'y')
let num16 = add.eq([ [int15,int1],[int14,int2],[int13,int3],[int12,int4],[int11,int5],[int10,int6],[int9,int7],[int8,int8] ],'y')
let num17 = add.eq([ [int16,int1],[int15,int2],[int14,int3],[int13,int4],[int12,int5],[int11,int6],[int10,int7],[int9,int8] ],'y')
let num18 = add.eq([ [int17,int1],[int16,int2],[int15,int3],[int14,int4],[int13,int5],[int12,int6],[int11,int7],[int10,int8],[int9,int9] ],'y')
let num19 = add.eq([ [int18,int1],[int17,int2],[int16,int3],[int15,int4],[int14,int5],[int13,int6],[int12,int7],[int11,int8],[int10,int9] ],'y')
let num20 = add.eq([ [int19,int1],[int18,int2],[int17,int3],[int16,int4],[int15,int5],[int14,int6],[int13,int7],[int12,int8],[int11,int9],[int10,int10] ],'y')
let num21 = add.eq([ [int20,int1],[int19,int2],[int18,int3],[int17,int4],[int16,int5],[int15,int6],[int14,int7],[int13,int8],[int12,int9],[int11,int10] ],'y')
let num22 = add.eq([ [int21,int1],[int20,int2],[int19,int3],[int18,int4],[int17,int5],[int16,int6],[int15,int7],[int14,int8],[int13,int9],[int12,int10],[int11,int11] ],'y')
let num23 = add.eq([ [int22,int1],[int21,int2],[int20,int3],[int19,int4],[int18,int5],[int17,int6],[int16,int7],[int15,int8],[int14,int9],[int13,int10],[int12,int11] ],'y')
let num24 = add.eq([ [int23,int1],[int22,int2],[int21,int3],[int20,int4],[int19,int5],[int18,int6],[int17,int7],[int16,int8],[int15,int9],[int14,int10],[int13,int11],[int12,int12] ],'y')
let num25 = add.eq([ [int24,int1],[int23,int2],[int22,int3],[int21,int4],[int20,int5],[int19,int6],[int18,int7],[int17,int8],[int16,int9],[int15,int10],[int14,int11],[int13,int12] ],'y')
let num26 = add.eq([ [int25,int1],[int24,int2],[int23,int3],[int22,int4],[int21,int5],[int20,int6],[int19,int7],[int18,int8],[int17,int9],[int16,int10],[int15,int11],[int14,int12],[int13,int13] ],'y')
let num27 = add.eq([ [int26,int1],[int25,int2],[int24,int3],[int23,int4],[int22,int5],[int21,int6],[int20,int7],[int19,int8],[int18,int9],[int17,int10],[int16,int11],[int15,int12],[int14,int13] ],'y')
let num28 = add.eq([ [int27,int1],[int26,int2],[int25,int3],[int24,int4],[int23,int5],[int22,int6],[int21,int7],[int20,int8],[int19,int9],[int18,int10],[int17,int11],[int16,int12],[int15,int13],[int14,int14] ],'y')
let num29 = add.eq([ [int28,int1],[int27,int2],[int26,int3],[int25,int4],[int24,int5],[int23,int6],[int22,int7],[int21,int8],[int20,int9],[int19,int10],[int18,int11],[int17,int12],[int16,int13],[int15,int14] ],'y')
let num30 = add.eq([ [int29,int1],[int28,int2],[int27,int3],[int26,int4],[int25,int5],[int24,int6],[int23,int7],[int22,int8],[int21,int9],[int20,int10],[int19,int11],[int18,int12],[int17,int13],[int16,int14],[int15,int15] ],'y')
let num31 = add.eq([ [int30,int1],[int29,int2],[int28,int3],[int27,int4],[int26,int5],[int25,int6],[int24,int7],[int23,int8],[int22,int9],[int21,int10],[int20,int11],[int19,int12],[int18,int13],[int17,int14],[int16,int15] ],'y')
let num32 = add.eq([ [int31,int1],[int30,int2],[int29,int3],[int28,int4],[int27,int5],[int26,int6],[int25,int7],[int24,int8],[int23,int9],[int22,int10],[int21,int11],[int20,int12],[int19,int13],[int18,int14],[int17,int15],[int16,int16] ],'y')
let num33 = add.eq([ [int32,int1],[int31,int2],[int30,int3],[int29,int4],[int28,int5],[int27,int6],[int26,int7],[int25,int8],[int24,int9],[int23,int10],[int22,int11],[int21,int12],[int20,int13],[int19,int14],[int18,int15],[int17,int16] ],'y')
let num34 = add.eq([ [int33,int1],[int32,int2],[int31,int3],[int30,int4],[int29,int5],[int28,int6],[int27,int7],[int26,int8],[int25,int9],[int24,int10],[int23,int11],[int22,int12],[int21,int13],[int20,int14],[int19,int15],[int18,int16],[int17,int17] ],'y')
let num35 = add.eq([ [int34,int1],[int33,int2],[int32,int3],[int31,int4],[int30,int5],[int29,int6],[int28,int7],[int27,int8],[int26,int9],[int25,int10],[int24,int11],[int23,int12],[int22,int13],[int21,int14],[int20,int15],[int19,int16],[int18,int17] ],'y')
let num36 = add.eq([ [int35,int1],[int34,int2],[int33,int3],[int32,int4],[int31,int5],[int30,int6],[int29,int7],[int28,int8],[int27,int9],[int26,int10],[int25,int11],[int24,int12],[int23,int13],[int22,int14],[int21,int15],[int20,int16],[int19,int17],[int18,int18] ],'y')
let num37 = add.eq([ [int36,int1],[int35,int2],[int34,int3],[int33,int4],[int32,int5],[int31,int6],[int30,int7],[int29,int8],[int28,int9],[int27,int10],[int26,int11],[int25,int12],[int24,int13],[int23,int14],[int22,int15],[int21,int16],[int20,int17],[int19,int18] ],'y')
let num38 = add.eq([ [int37,int1],[int36,int2],[int35,int3],[int34,int4],[int33,int5],[int32,int6],[int31,int7],[int30,int8],[int29,int9],[int28,int10],[int27,int11],[int26,int12],[int25,int13],[int24,int14],[int23,int15],[int22,int16],[int21,int17],[int20,int18],[int19,int19] ],'y')
let num39 = add.eq([ [int38,int1],[int37,int2],[int36,int3],[int35,int4],[int34,int5],[int33,int6],[int32,int7],[int31,int8],[int30,int9],[int29,int10],[int28,int11],[int27,int12],[int26,int13],[int25,int14],[int24,int15],[int23,int16],[int22,int17],[int21,int18],[int20,int19] ],'y')
let num40 = add.eq([ [int39,int1],[int38,int2],[int37,int3],[int36,int4],[int35,int5],[int34,int6],[int33,int7],[int32,int8],[int31,int9],[int30,int10],[int29,int11],[int28,int12],[int27,int13],[int26,int14],[int25,int15],[int24,int16],[int23,int17],[int22,int18],[int21,int19],[int20,int20] ],'y')
let num41 = add.eq([ [int40,int1],[int39,int2],[int38,int3],[int37,int4],[int36,int5],[int35,int6],[int34,int7],[int33,int8],[int32,int9],[int31,int10],[int30,int11],[int29,int12],[int28,int13],[int27,int14],[int26,int15],[int25,int16],[int24,int17],[int23,int18],[int22,int19],[int21,int20] ],'y')
let num42 = add.eq([ [int41,int1],[int40,int2],[int39,int3],[int38,int4],[int37,int5],[int36,int6],[int35,int7],[int34,int8],[int33,int9],[int32,int10],[int31,int11],[int30,int12],[int29,int13],[int28,int14],[int27,int15],[int26,int16],[int25,int17],[int24,int18],[int23,int19],[int22,int20],[int21,int21] ],'y')
let num43 = add.eq([ [int42,int1],[int41,int2],[int40,int3],[int39,int4],[int38,int5],[int37,int6],[int36,int7],[int35,int8],[int34,int9],[int33,int10],[int32,int11],[int31,int12],[int30,int13],[int29,int14],[int28,int15],[int27,int16],[int26,int17],[int25,int18],[int24,int19],[int23,int20],[int22,int21] ],'y')
let num44 = add.eq([ [int43,int1],[int42,int2],[int41,int3],[int40,int4],[int39,int5],[int38,int6],[int37,int7],[int36,int8],[int35,int9],[int34,int10],[int33,int11],[int32,int12],[int31,int13],[int30,int14],[int29,int15],[int28,int16],[int27,int17],[int26,int18],[int25,int19],[int24,int20],[int23,int21],[int22,int22] ],'y')
let num45 = add.eq([ [int44,int1],[int43,int2],[int42,int3],[int41,int4],[int40,int5],[int39,int6],[int38,int7],[int37,int8],[int36,int9],[int35,int10],[int34,int11],[int33,int12],[int32,int13],[int31,int14],[int30,int15],[int29,int16],[int28,int17],[int27,int18],[int26,int19],[int25,int20],[int24,int21],[int23,int22] ],'y')
let num46 = add.eq([ [int45,int1],[int44,int2],[int43,int3],[int42,int4],[int41,int5],[int40,int6],[int39,int7],[int38,int8],[int37,int9],[int36,int10],[int35,int11],[int34,int12],[int33,int13],[int32,int14],[int31,int15],[int30,int16],[int29,int17],[int28,int18],[int27,int19],[int26,int20],[int25,int21],[int24,int22],[int23,int23] ],'y')
let num47 = add.eq([ [int46,int1],[int45,int2],[int44,int3],[int43,int4],[int42,int5],[int41,int6],[int40,int7],[int39,int8],[int38,int9],[int37,int10],[int36,int11],[int35,int12],[int34,int13],[int33,int14],[int32,int15],[int31,int16],[int30,int17],[int29,int18],[int28,int19],[int27,int20],[int26,int21],[int25,int22],[int24,int23] ],'y')
let num48 = add.eq([ [int47,int1],[int46,int2],[int45,int3],[int44,int4],[int43,int5],[int42,int6],[int41,int7],[int40,int8],[int39,int9],[int38,int10],[int37,int11],[int36,int12],[int35,int13],[int34,int14],[int33,int15],[int32,int16],[int31,int17],[int30,int18],[int29,int19],[int28,int20],[int27,int21],[int26,int22],[int25,int23],[int24,int24] ],'y')
let num49 = add.eq([ [int48,int1],[int47,int2],[int46,int3],[int45,int4],[int44,int5],[int43,int6],[int42,int7],[int41,int8],[int40,int9],[int39,int10],[int38,int11],[int37,int12],[int36,int13],[int35,int14],[int34,int15],[int33,int16],[int32,int17],[int31,int18],[int30,int19],[int29,int20],[int28,int21],[int27,int22],[int26,int23],[int25,int24] ],'y')
let num50 = add.eq([ [int49,int1],[int48,int2],[int47,int3],[int46,int4],[int45,int5],[int44,int6],[int43,int7],[int42,int8],[int41,int9],[int40,int10],[int39,int11],[int38,int12],[int37,int13],[int36,int14],[int35,int15],[int34,int16],[int33,int17],[int32,int18],[int31,int19],[int30,int20],[int29,int21],[int28,int22],[int27,int23],[int26,int24],[int25,int25] ],'y')
let num51 = add.eq([ [int50,int1],[int49,int2],[int48,int3],[int47,int4],[int46,int5],[int45,int6],[int44,int7],[int43,int8],[int42,int9],[int41,int10],[int40,int11],[int39,int12],[int38,int13],[int37,int14],[int36,int15],[int35,int16],[int34,int17],[int33,int18],[int32,int19],[int31,int20],[int30,int21],[int29,int22],[int28,int23],[int27,int24],[int26,int25] ],'y')
let num52 = add.eq([ [int51,int1],[int50,int2],[int49,int3],[int48,int4],[int47,int5],[int46,int6],[int45,int7],[int44,int8],[int43,int9],[int42,int10],[int41,int11],[int40,int12],[int39,int13],[int38,int14],[int37,int15],[int36,int16],[int35,int17],[int34,int18],[int33,int19],[int32,int20],[int31,int21],[int30,int22],[int29,int23],[int28,int24],[int27,int25],[int26,int26] ],'y')
let num53 = add.eq([ [int52,int1],[int51,int2],[int50,int3],[int49,int4],[int48,int5],[int47,int6],[int46,int7],[int45,int8],[int44,int9],[int43,int10],[int42,int11],[int41,int12],[int40,int13],[int39,int14],[int38,int15],[int37,int16],[int36,int17],[int35,int18],[int34,int19],[int33,int20],[int32,int21],[int31,int22],[int30,int23],[int29,int24],[int28,int25],[int27,int26] ],'y')
let num54 = add.eq([ [int53,int1],[int52,int2],[int51,int3],[int50,int4],[int49,int5],[int48,int6],[int47,int7],[int46,int8],[int45,int9],[int44,int10],[int43,int11],[int42,int12],[int41,int13],[int40,int14],[int39,int15],[int38,int16],[int37,int17],[int36,int18],[int35,int19],[int34,int20],[int33,int21],[int32,int22],[int31,int23],[int30,int24],[int29,int25],[int28,int26],[int27,int27] ],'y')
let num55 = add.eq([ [int54,int1],[int53,int2],[int52,int3],[int51,int4],[int50,int5],[int49,int6],[int48,int7],[int47,int8],[int46,int9],[int45,int10],[int44,int11],[int43,int12],[int42,int13],[int41,int14],[int40,int15],[int39,int16],[int38,int17],[int37,int18],[int36,int19],[int35,int20],[int34,int21],[int33,int22],[int32,int23],[int31,int24],[int30,int25],[int29,int26],[int28,int27] ],'y')
let num56 = add.eq([ [int55,int1],[int54,int2],[int53,int3],[int52,int4],[int51,int5],[int50,int6],[int49,int7],[int48,int8],[int47,int9],[int46,int10],[int45,int11],[int44,int12],[int43,int13],[int42,int14],[int41,int15],[int40,int16],[int39,int17],[int38,int18],[int37,int19],[int36,int20],[int35,int21],[int34,int22],[int33,int23],[int32,int24],[int31,int25],[int30,int26],[int29,int27],[int28,int28] ],'y')
let num57 = add.eq([ [int56,int1],[int55,int2],[int54,int3],[int53,int4],[int52,int5],[int51,int6],[int50,int7],[int49,int8],[int48,int9],[int47,int10],[int46,int11],[int45,int12],[int44,int13],[int43,int14],[int42,int15],[int41,int16],[int40,int17],[int39,int18],[int38,int19],[int37,int20],[int36,int21],[int35,int22],[int34,int23],[int33,int24],[int32,int25],[int31,int26],[int30,int27],[int29,int28] ],'y')
let num58 = add.eq([ [int57,int1],[int56,int2],[int55,int3],[int54,int4],[int53,int5],[int52,int6],[int51,int7],[int50,int8],[int49,int9],[int48,int10],[int47,int11],[int46,int12],[int45,int13],[int44,int14],[int43,int15],[int42,int16],[int41,int17],[int40,int18],[int39,int19],[int38,int20],[int37,int21],[int36,int22],[int35,int23],[int34,int24],[int33,int25],[int32,int26],[int31,int27],[int30,int28],[int29,int29] ],'y')
let num59 = add.eq([ [int58,int1],[int57,int2],[int56,int3],[int55,int4],[int54,int5],[int53,int6],[int52,int7],[int51,int8],[int50,int9],[int49,int10],[int48,int11],[int47,int12],[int46,int13],[int45,int14],[int44,int15],[int43,int16],[int42,int17],[int41,int18],[int40,int19],[int39,int20],[int38,int21],[int37,int22],[int36,int23],[int35,int24],[int34,int25],[int33,int26],[int32,int27],[int31,int28],[int30,int29] ],'y')
let num60 = add.eq([ [int59,int1],[int58,int2],[int57,int3],[int56,int4],[int55,int5],[int54,int6],[int53,int7],[int52,int8],[int51,int9],[int50,int10],[int49,int11],[int48,int12],[int47,int13],[int46,int14],[int45,int15],[int44,int16],[int43,int17],[int42,int18],[int41,int19],[int40,int20],[int39,int21],[int38,int22],[int37,int23],[int36,int24],[int35,int25],[int34,int26],[int33,int27],[int32,int28],[int31,int29],[int30,int30] ],'y')
let num61 = add.eq([ [int60,int1],[int59,int2],[int58,int3],[int57,int4],[int56,int5],[int55,int6],[int54,int7],[int53,int8],[int52,int9],[int51,int10],[int50,int11],[int49,int12],[int48,int13],[int47,int14],[int46,int15],[int45,int16],[int44,int17],[int43,int18],[int42,int19],[int41,int20],[int40,int21],[int39,int22],[int38,int23],[int37,int24],[int36,int25],[int35,int26],[int34,int27],[int33,int28],[int32,int29],[int31,int30] ],'y')
let num62 = add.eq([ [int61,int1],[int60,int2],[int59,int3],[int58,int4],[int57,int5],[int56,int6],[int55,int7],[int54,int8],[int53,int9],[int52,int10],[int51,int11],[int50,int12],[int49,int13],[int48,int14],[int47,int15],[int46,int16],[int45,int17],[int44,int18],[int43,int19],[int42,int20],[int41,int21],[int40,int22],[int39,int23],[int38,int24],[int37,int25],[int36,int26],[int35,int27],[int34,int28],[int33,int29],[int32,int30],[int31,int31] ],'y')
let num63 = add.eq([ [int62,int1],[int61,int2],[int60,int3],[int59,int4],[int58,int5],[int57,int6],[int56,int7],[int55,int8],[int54,int9],[int53,int10],[int52,int11],[int51,int12],[int50,int13],[int49,int14],[int48,int15],[int47,int16],[int46,int17],[int45,int18],[int44,int19],[int43,int20],[int42,int21],[int41,int22],[int40,int23],[int39,int24],[int38,int25],[int37,int26],[int36,int27],[int35,int28],[int34,int29],[int33,int30],[int32,int31] ],'y')
let num64 = add.eq([ [int63,int1],[int62,int2],[int61,int3],[int60,int4],[int59,int5],[int58,int6],[int57,int7],[int56,int8],[int55,int9],[int54,int10],[int53,int11],[int52,int12],[int51,int13],[int50,int14],[int49,int15],[int48,int16],[int47,int17],[int46,int18],[int45,int19],[int44,int20],[int43,int21],[int42,int22],[int41,int23],[int40,int24],[int39,int25],[int38,int26],[int37,int27],[int36,int28],[int35,int29],[int34,int30],[int33,int31],[int32,int32] ],'y')
let num65 = add.eq([ [int64,int1],[int63,int2],[int62,int3],[int61,int4],[int60,int5],[int59,int6],[int58,int7],[int57,int8],[int56,int9],[int55,int10],[int54,int11],[int53,int12],[int52,int13],[int51,int14],[int50,int15],[int49,int16],[int48,int17],[int47,int18],[int46,int19],[int45,int20],[int44,int21],[int43,int22],[int42,int23],[int41,int24],[int40,int25],[int39,int26],[int38,int27],[int37,int28],[int36,int29],[int35,int30],[int34,int31],[int33,int32] ],'y')
let num66 = add.eq([ [int65,int1],[int64,int2],[int63,int3],[int62,int4],[int61,int5],[int60,int6],[int59,int7],[int58,int8],[int57,int9],[int56,int10],[int55,int11],[int54,int12],[int53,int13],[int52,int14],[int51,int15],[int50,int16],[int49,int17],[int48,int18],[int47,int19],[int46,int20],[int45,int21],[int44,int22],[int43,int23],[int42,int24],[int41,int25],[int40,int26],[int39,int27],[int38,int28],[int37,int29],[int36,int30],[int35,int31],[int34,int32],[int33,int33] ],'y')
let num67 = add.eq([ [int66,int1],[int65,int2],[int64,int3],[int63,int4],[int62,int5],[int61,int6],[int60,int7],[int59,int8],[int58,int9],[int57,int10],[int56,int11],[int55,int12],[int54,int13],[int53,int14],[int52,int15],[int51,int16],[int50,int17],[int49,int18],[int48,int19],[int47,int20],[int46,int21],[int45,int22],[int44,int23],[int43,int24],[int42,int25],[int41,int26],[int40,int27],[int39,int28],[int38,int29],[int37,int30],[int36,int31],[int35,int32],[int34,int33] ],'y')
let num68 = add.eq([ [int67,int1],[int66,int2],[int65,int3],[int64,int4],[int63,int5],[int62,int6],[int61,int7],[int60,int8],[int59,int9],[int58,int10],[int57,int11],[int56,int12],[int55,int13],[int54,int14],[int53,int15],[int52,int16],[int51,int17],[int50,int18],[int49,int19],[int48,int20],[int47,int21],[int46,int22],[int45,int23],[int44,int24],[int43,int25],[int42,int26],[int41,int27],[int40,int28],[int39,int29],[int38,int30],[int37,int31],[int36,int32],[int35,int33],[int34,int34] ],'y')
let num69 = add.eq([ [int68,int1],[int67,int2],[int66,int3],[int65,int4],[int64,int5],[int63,int6],[int62,int7],[int61,int8],[int60,int9],[int59,int10],[int58,int11],[int57,int12],[int56,int13],[int55,int14],[int54,int15],[int53,int16],[int52,int17],[int51,int18],[int50,int19],[int49,int20],[int48,int21],[int47,int22],[int46,int23],[int45,int24],[int44,int25],[int43,int26],[int42,int27],[int41,int28],[int40,int29],[int39,int30],[int38,int31],[int37,int32],[int36,int33],[int35,int34] ],'y')
let num70 = add.eq([ [int69,int1],[int68,int2],[int67,int3],[int66,int4],[int65,int5],[int64,int6],[int63,int7],[int62,int8],[int61,int9],[int60,int10],[int59,int11],[int58,int12],[int57,int13],[int56,int14],[int55,int15],[int54,int16],[int53,int17],[int52,int18],[int51,int19],[int50,int20],[int49,int21],[int48,int22],[int47,int23],[int46,int24],[int45,int25],[int44,int26],[int43,int27],[int42,int28],[int41,int29],[int40,int30],[int39,int31],[int38,int32],[int37,int33],[int36,int34],[int35,int35] ],'y')
let num71 = add.eq([ [int70,int1],[int69,int2],[int68,int3],[int67,int4],[int66,int5],[int65,int6],[int64,int7],[int63,int8],[int62,int9],[int61,int10],[int60,int11],[int59,int12],[int58,int13],[int57,int14],[int56,int15],[int55,int16],[int54,int17],[int53,int18],[int52,int19],[int51,int20],[int50,int21],[int49,int22],[int48,int23],[int47,int24],[int46,int25],[int45,int26],[int44,int27],[int43,int28],[int42,int29],[int41,int30],[int40,int31],[int39,int32],[int38,int33],[int37,int34],[int36,int35] ],'y')
let num72 = add.eq([ [int71,int1],[int70,int2],[int69,int3],[int68,int4],[int67,int5],[int66,int6],[int65,int7],[int64,int8],[int63,int9],[int62,int10],[int61,int11],[int60,int12],[int59,int13],[int58,int14],[int57,int15],[int56,int16],[int55,int17],[int54,int18],[int53,int19],[int52,int20],[int51,int21],[int50,int22],[int49,int23],[int48,int24],[int47,int25],[int46,int26],[int45,int27],[int44,int28],[int43,int29],[int42,int30],[int41,int31],[int40,int32],[int39,int33],[int38,int34],[int37,int35],[int36,int36] ],'y')
let num73 = add.eq([ [int72,int1],[int71,int2],[int70,int3],[int69,int4],[int68,int5],[int67,int6],[int66,int7],[int65,int8],[int64,int9],[int63,int10],[int62,int11],[int61,int12],[int60,int13],[int59,int14],[int58,int15],[int57,int16],[int56,int17],[int55,int18],[int54,int19],[int53,int20],[int52,int21],[int51,int22],[int50,int23],[int49,int24],[int48,int25],[int47,int26],[int46,int27],[int45,int28],[int44,int29],[int43,int30],[int42,int31],[int41,int32],[int40,int33],[int39,int34],[int38,int35],[int37,int36] ],'y')
let num74 = add.eq([ [int73,int1],[int72,int2],[int71,int3],[int70,int4],[int69,int5],[int68,int6],[int67,int7],[int66,int8],[int65,int9],[int64,int10],[int63,int11],[int62,int12],[int61,int13],[int60,int14],[int59,int15],[int58,int16],[int57,int17],[int56,int18],[int55,int19],[int54,int20],[int53,int21],[int52,int22],[int51,int23],[int50,int24],[int49,int25],[int48,int26],[int47,int27],[int46,int28],[int45,int29],[int44,int30],[int43,int31],[int42,int32],[int41,int33],[int40,int34],[int39,int35],[int38,int36],[int37,int37] ],'y')
let num75 = add.eq([ [int74,int1],[int73,int2],[int72,int3],[int71,int4],[int70,int5],[int69,int6],[int68,int7],[int67,int8],[int66,int9],[int65,int10],[int64,int11],[int63,int12],[int62,int13],[int61,int14],[int60,int15],[int59,int16],[int58,int17],[int57,int18],[int56,int19],[int55,int20],[int54,int21],[int53,int22],[int52,int23],[int51,int24],[int50,int25],[int49,int26],[int48,int27],[int47,int28],[int46,int29],[int45,int30],[int44,int31],[int43,int32],[int42,int33],[int41,int34],[int40,int35],[int39,int36],[int38,int37] ],'y')
let num76 = add.eq([ [int75,int1],[int74,int2],[int73,int3],[int72,int4],[int71,int5],[int70,int6],[int69,int7],[int68,int8],[int67,int9],[int66,int10],[int65,int11],[int64,int12],[int63,int13],[int62,int14],[int61,int15],[int60,int16],[int59,int17],[int58,int18],[int57,int19],[int56,int20],[int55,int21],[int54,int22],[int53,int23],[int52,int24],[int51,int25],[int50,int26],[int49,int27],[int48,int28],[int47,int29],[int46,int30],[int45,int31],[int44,int32],[int43,int33],[int42,int34],[int41,int35],[int40,int36],[int39,int37],[int38,int38] ],'y')
let num77 = add.eq([ [int76,int1],[int75,int2],[int74,int3],[int73,int4],[int72,int5],[int71,int6],[int70,int7],[int69,int8],[int68,int9],[int67,int10],[int66,int11],[int65,int12],[int64,int13],[int63,int14],[int62,int15],[int61,int16],[int60,int17],[int59,int18],[int58,int19],[int57,int20],[int56,int21],[int55,int22],[int54,int23],[int53,int24],[int52,int25],[int51,int26],[int50,int27],[int49,int28],[int48,int29],[int47,int30],[int46,int31],[int45,int32],[int44,int33],[int43,int34],[int42,int35],[int41,int36],[int40,int37],[int39,int38] ],'y')
let num78 = add.eq([ [int77,int1],[int76,int2],[int75,int3],[int74,int4],[int73,int5],[int72,int6],[int71,int7],[int70,int8],[int69,int9],[int68,int10],[int67,int11],[int66,int12],[int65,int13],[int64,int14],[int63,int15],[int62,int16],[int61,int17],[int60,int18],[int59,int19],[int58,int20],[int57,int21],[int56,int22],[int55,int23],[int54,int24],[int53,int25],[int52,int26],[int51,int27],[int50,int28],[int49,int29],[int48,int30],[int47,int31],[int46,int32],[int45,int33],[int44,int34],[int43,int35],[int42,int36],[int41,int37],[int40,int38],[int39,int39] ],'y')
let num79 = add.eq([ [int78,int1],[int77,int2],[int76,int3],[int75,int4],[int74,int5],[int73,int6],[int72,int7],[int71,int8],[int70,int9],[int69,int10],[int68,int11],[int67,int12],[int66,int13],[int65,int14],[int64,int15],[int63,int16],[int62,int17],[int61,int18],[int60,int19],[int59,int20],[int58,int21],[int57,int22],[int56,int23],[int55,int24],[int54,int25],[int53,int26],[int52,int27],[int51,int28],[int50,int29],[int49,int30],[int48,int31],[int47,int32],[int46,int33],[int45,int34],[int44,int35],[int43,int36],[int42,int37],[int41,int38],[int40,int39] ],'y')
let num80 = add.eq([ [int79,int1],[int78,int2],[int77,int3],[int76,int4],[int75,int5],[int74,int6],[int73,int7],[int72,int8],[int71,int9],[int70,int10],[int69,int11],[int68,int12],[int67,int13],[int66,int14],[int65,int15],[int64,int16],[int63,int17],[int62,int18],[int61,int19],[int60,int20],[int59,int21],[int58,int22],[int57,int23],[int56,int24],[int55,int25],[int54,int26],[int53,int27],[int52,int28],[int51,int29],[int50,int30],[int49,int31],[int48,int32],[int47,int33],[int46,int34],[int45,int35],[int44,int36],[int43,int37],[int42,int38],[int41,int39],[int40,int40] ],'y')
20

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