Commit b552e184 authored by Charles Bouillaguet's avatar Charles Bouillaguet
Browse files

for publication

parent f562b4fe
CC = gcc
CFLAGS = -std=c11 -g -Wall -Wextra -O3 -Wno-unused-parameter -Werror -march=native -mavx2
CFLAGS = -std=c11 -g -Wall -Wextra -O3 -Wno-unused-parameter -Wno-maybe-uninitialized -Werror -march=native -mavx2
# OpenMP
CFLAGS += -fopenmp
LDFLAGS += -fopenmp
LDLIBS += -lm
all: parser_demo parser_demo_alt moebius_demo monica monica_packed monica_oblivious
all: parser_demo parser_demo_alt moebius_demo monica monica_vector
monica: parser.o monica.o
monica_packed: parser.o monica_packed.o
monica_oblivious: parser.o monica_oblivious.o
monica_vector: parser.o monica_vector.o
parser_demo: parser.o parser_demo.o
parser_demo_alt: parser.o parser_demo_alt.o
moebius_demo: parser.o moebius.o moebius_demo.o
moebius_demo.o: parser.h moebius.h
parser_demo.o: parser.h
parser.o: parser.h
moebius.o: moebius.h
monica.o: parser.h ffs.h
monica_packed.o: parser.h ffs.h
monica_oblivious.o: parser.h ffs.h
monica_vector.o: parser.h ffs.h
clean:
rm -f *.o
rm -f parser_demo moebius_demo parser_demo_alt monica monica_packed monica_oblivious
rm -f parser_demo moebius_demo parser_demo_alt monica monica_vector
# Programs for solving Boolean polynomial systems
This code is in the public domain. Several algorithms are implemented.
Exhaustive search is available elsewhere, in the [libfes-lite](https://gitlab.lip6.fr/almasty/libfes-lite) library.
# Monica
This program implements a striped-down version of the [Crossbred algorithm of Joux-Vitse](https://hal.archives-ouvertes.fr/PRISM/hal-01981516v1). It handles at most 64 variables. At this point, it is not multi-threaded.
Internally, it uses "libfes-style" gray-code enumeration to evaluate polynomials quickly.
There are two versions : `monica.c`, which is as simple as possible, and `monica_vector.c`,
which tries to use the fact that several bits fits into a single word to speed things up.
The most important parameter is `--inner-hybridation`, which specifies how
many variables are not guessed. It may make sense to try one less than the default value.
Example:
```
./monica_vector --inner-hybridation 7 < examples/random_40_quad.in
```
# Moebius
This small piece of code solves systems of arbitrary-degree boolean
polynomials, by "exhaustive search", using the moebius transform algorithm.
This code is in the public domain.
The example program requires a C11-capable compiler (because it uses `aligned_alloc`).
It is multi-threaded, using OpenMP. By default, it will run one thread by "processor",
which means per logical core.
......@@ -19,6 +42,7 @@ Example:
# ./moebius_demo < examples/large.in
```
# Input format
This code parses polynomial systems modulo 2 in the following format:
......@@ -34,17 +58,8 @@ This code parses polynomial systems modulo 2 in the following format:
(It follows that an empty line denote the zero polynomial).
# Parser
The parser is somewhat generic and could be useful in other contexts.
See `parser_demo.c` and `parser_demo_alt.c` for examples of use.
# Monica
This program implements a striped-down the algorithm of Monica Trimoska for quadratic
polynomials. It handles <= 64 variables. At this point, it is not multi-threaded.
Internally, it uses "libfes-style" gray-code enumeration to evaluate polynomials quickly.
There are two versions : `monica.c`, which is a simple as possible, and `monica_packed.c`,
which tries to use the fact that several bits fits into a single word to speed things up.
\ No newline at end of file
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# planted solution: (0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1)
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x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38,x39
# planted solution: (1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0)
x0*x4 + x0*x5 + x0*x6 + x0*x7 + x0*x11 + x0*x12 + x0*x13 + x0*x14 + x0*x16 + x0*x18 + x0*x21 + x0*x22 + x0*x23 + x0*x24 + x0*x25 + x0*x27 + x0*x29 + x0*x31 + x0*x34 + x0*x37 + x0*x38 + x0*x39 + x0 + x1*x5 + x1*x7 + x1*x8 + x1*x9 + x1*x12 + x1*x13 + x1*x15 + x1*x16 + x1*x18 + x1*x19 + x1*x20 + x1*x22 + x1*x25 + x1*x29 + x1*x32 + x1*x34 + x1*x37 + x1*x39 + x1 + x2*x4 + x2*x7 + x2*x9 + x2*x10 + x2*x13 + x2*x16 + x2*x17 + x2*x18 + x2*x22 + x2*x23 + x2*x24 + x2*x26 + x2*x27 + x2*x28 + x2*x29 + x2*x33 + x2*x34 + x2*x35 + x2*x36 + x2*x38 + x2*x39 + x2 + x3*x4 + x3*x5 + x3*x8 + x3*x10 + x3*x11 + x3*x12 + x3*x13 + x3*x14 + x3*x15 + x3*x19 + x3*x20 + x3*x22 + x3*x23 + x3*x24 + x3*x27 + x3*x35 + x3*x37 + x3*x39 + x3 + x4*x5 + x4*x6 + x4*x7 + x4*x8 + x4*x9 + x4*x12 + x4*x13 + x4*x14 + x4*x15 + x4*x16 + x4*x17 + x4*x19 + x4*x21 + x4*x22 + x4*x23 + x4*x27 + x4*x29 + x4*x30 + x4*x31 + x4*x32 + x4*x34 + x4*x38 + x5*x10 + x5*x12 + x5*x13 + x5*x14 + x5*x17 + x5*x19 + x5*x20 + x5*x21 + x5*x23 + x5*x24 + x5*x28 + x5*x30 + x5*x33 + x5*x34 + x5*x36 + x5*x37 + x6*x9 + x6*x12 + x6*x13 + x6*x16 + x6*x18 + x6*x19 + x6*x20 + x6*x22 + x6*x26 + x6*x28 + x6*x31 + x6*x33 + x6*x34 + x6*x35 + x6*x37 + x6*x38 + x6*x39 + x7*x8 + x7*x10 + x7*x13 + x7*x15 + x7*x16 + x7*x17 + x7*x23 + x7*x25 + x7*x26 + x7*x29 + x7*x33 + x7*x36 + x7*x37 + x7*x38 + x7*x39 + x8*x10 + x8*x14 + x8*x16 + x8*x17 + x8*x18 + x8*x22 + x8*x24 + x8*x25 + x8*x26 + x8*x29 + x8*x33 + x8*x34 + x8*x35 + x8*x37 + x8*x38 + x8*x39 + x8 + x9*x11 + x9*x12 + x9*x15 + x9*x16 + x9*x20 + x9*x24 + x9*x28 + x9*x30 + x9*x31 + x9*x37 + x9*x38 + x9*x39 + x10*x13 + x10*x14 + x10*x16 + x10*x17 + x10*x19 + x10*x23 + x10*x24 + x10*x25 + x10*x26 + x10*x27 + x10*x28 + x10*x29 + x10*x33 + x10*x35 + x10*x37 + x10*x38 + x10*x39 + x11*x12 + x11*x14 + x11*x15 + x11*x19 + x11*x22 + x11*x23 + x11*x24 + x11*x25 + x11*x26 + x11*x29 + x11*x31 + x11*x35 + x11*x37 + x11*x38 + x11*x39 + x11 + x12*x13 + x12*x14 + x12*x15 + x12*x19 + x12*x20 + x12*x21 + x12*x22 + x12*x23 + x12*x26 + x12*x28 + x12*x31 + x12*x33 + x12*x35 + x12*x37 + x13*x19 + x13*x20 + x13*x21 + x13*x24 + x13*x29 + x13*x31 + x13*x37 + x13*x38 + x13 + x14*x15 + x14*x16 + x14*x19 + x14*x20 + x14*x23 + x14*x24 + x14*x26 + x14*x29 + x14*x31 + x14*x35 + x14*x37 + x15*x19 + x15*x20 + x15*x22 + x15*x24 + x15*x25 + x15*x29 + x15*x31 + x15*x32 + x15*x36 + x15*x37 + x15*x38 + x15*x39 + x16*x18 + x16*x19 + x16*x20 + x16*x21 + x16*x23 + x16*x25 + x16*x26 + x16*x30 + x16*x38 + x17*x20 + x17*x21 + x17*x22 + x17*x25 + x17*x27 + x17*x29 + x17*x31 + x17*x32 + x17*x34 + x17*x35 + x17*x38 + x17*x39 + x18*x22 + x18*x24 + x18*x30 + x18*x31 + x18*x32 + x18*x33 + x18*x34 + x18*x35 + x18*x37 + x18 + x19*x20 + x19*x22 + x19*x24 + x19*x25 + x19*x28 + x19*x29 + x19*x33 + x19*x35 + x19*x38 + x19*x39 + x19 + x20*x21 + x20*x24 + x20*x26 + x20*x30 + x20*x31 + x20*x33 + x20*x34 + x20*x35 + x21*x26 + x21*x27 + x21*x28 + x21*x33 + x21*x34 + x21*x38 + x21*x39 + x21 + x22*x23 + x22*x24 + x22*x27 + x22*x28 + x22*x29 + x22*x30 + x22*x31 + x22*x32 + x22*x33 + x22*x35 + x22*x37 + x23*x25 + x23*x26 + x23*x29 + x23*x30 + x23*x31 + x23*x32 + x23*x33 + x23*x39 + x24*x26 + x24*x27 + x24*x28 + x24*x29 + x24*x30 + x24*x33 + x24*x34 + x24*x35 + x24*x38 + x24 + x25*x27 + x25*x29 + x25*x30 + x25*x31 + x25*x33 + x25*x34 + x25*x36 + x25*x37 + x25 + x26*x30 + x26*x31 + x26*x34 + x26*x36 + x26*x37 + x26*x39 + x27*x28 + x27*x29 + x27*x30 + x27*x32 + x27*x35 + x27*x36 + x28*x29 + x28*x33 + x28*x35 + x28*x37 + x29*x31 + x29*x34 + x29*x35 + x29*x36 + x29*x37 + x29*x38 + x29*x39 + x29 + x30*x33 + x30*x35 + x30*x36 + x30*x37 + x30*x38 + x30*x39 + x31*x32 + x31*x36 + x31*x37 + x31*x38 + x32*x33 + x32*x34 + x32*x38 + x33*x35 + x33*x37 + x33 + x34*x38 + x34*x39 + x35*x37 + x35*x38 + x35*x39 + x35 + x36*x37 + x37*x39 + x37 + x38 + x39 + 1
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x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38,x39
# planted solution: (1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1)
x0*x1 + x0*x4 + x0*x5 + x0*x7 + x0*x8 + x0*x11 + x0*x13 + x0*x14 + x0*x15 + x0*x16 + x0*x17 + x0*x19 + x0*x20 + x0*x24 + x0*x27 + x0*x29 + x0*x31 + x0*x32 + x0*x36 + x0*x37 + x1*x3 + x1*x5 + x1*x8 + x1*x9 + x1*x11 + x1*x15 + x1*x18 + x1*x20 + x1*x21 + x1*x26 + x1*x27 + x1*x29 + x1*x30 + x1*x31 + x1*x35 + x2*x3 + x2*x5 + x2*x6 + x2*x10 + x2*x12 + x2*x13 + x2*x14 + x2*x18 + x2*x19 + x2*x21 + x2*x22 + x2*x23 + x2*x24 + x2*x25 + x2*x26 + x2*x28 + x2*x33 + x2*x36 + x2*x37 + x2*x38 + x3*x4 + x3*x5 + x3*x7 + x3*x9 + x3*x11 + x3*x13 + x3*x15 + x3*x16 + x3*x17 + x3*x18 + x3*x23 + x3*x24 + x3*x25 + x3*x26 + x3*x28 + x3*x31 + x3*x33 + x3*x36 + x3*x37 + x3 + x4*x9 + x4*x10 + x4*x11 + x4*x12 + x4*x13 + x4*x17 + x4*x18 + x4*x19 + x4*x21 + x4*x22 + x4*x23 + x4*x25 + x4*x26 + x4*x28 + x4*x29 + x4*x30 + x4*x31 + x4*x32 + x4*x34 + x4*x37 + x4*x38 + x5*x6 + x5*x7 + x5*x10 + x5*x11 + x5*x13 + x5*x14 + x5*x15 + x5*x17 + x5*x21 + x5*x22 + x5*x28 + x5*x30 + x5*x32 + x5*x37 + x6*x7 + x6*x12 + x6*x16 + x6*x17 + x6*x18 + x6*x19 + x6*x20 + x6*x21 + x6*x22 + x6*x24 + x6*x26 + x6*x29 + x6*x31 + x6*x33 + x6*x35 + x6*x37 + x6*x38 + x6*x39 + x7*x8 + x7*x9 + x7*x13 + x7*x14 + x7*x15 + x7*x17 + x7*x20 + x7*x21 + x7*x23 + x7*x24 + x7*x27 + x7*x28 + x7*x30 + x7*x32 + x7*x34 + x7*x39 + x7 + x8*x10 + x8*x12 + x8*x13 + x8*x16 + x8*x17 + x8*x18 + x8*x19 + x8*x21 + x8*x22 + x8*x27 + x8*x28 + x8*x29 + x8*x37 + x8*x39 + x8 + x9*x10 + x9*x11 + x9*x12 + x9*x14 + x9*x15 + x9*x18 + x9*x19 + x9*x24 + x9*x25 + x9*x27 + x9*x28 + x9*x29 + x9*x30 + x9*x31 + x9*x32 + x9 + x10*x13 + x10*x15 + x10*x17 + x10*x19 + x10*x20 + x10*x21 + x10*x22 + x10*x25 + x10*x29 + x10*x33 + x10*x34 + x10*x36 + x10*x37 + x10*x39 + x11*x13 + x11*x14 + x11*x15 + x11*x16 + x11*x17 + x11*x18 + x11*x20 + x11*x21 + x11*x25 + x11*x26 + x11*x27 + x11*x28 + x11*x29 + x11*x30 + x11 + x12*x13 + x12*x18 + x12*x19 + x12*x20 + x12*x25 + x12*x26 + x12*x30 + x12*x31 + x12*x34 + x12*x35 + x12*x36 + x12*x37 + x12*x38 + x12 + x13*x14 + x13*x17 + x13*x18 + x13*x22 + x13*x24 + x13*x28 + x13*x29 + x13*x30 + x13*x31 + x13*x35 + x13 + x14*x16 + x14*x19 + x14*x21 + x14*x23 + x14*x24 + x14*x25 + x14*x26 + x14*x31 + x14*x34 + x14*x35 + x14*x37 + x14*x38 + x14*x39 + x15*x17 + x15*x18 + x15*x19 + x15*x23 + x15*x24 + x15*x25 + x15*x26 + x15*x30 + x15*x32 + x15*x35 + x15*x36 + x15*x37 + x15*x38 + x16*x18 + x16*x19 + x16*x20 + x16*x22 + x16*x24 + x16*x25 + x16*x28 + x16*x30 + x16*x31 + x16*x32 + x16*x33 + x16*x37 + x16*x38 + x16*x39 + x17*x22 + x17*x23 + x17*x26 + x17*x28 + x17*x29 + x17*x30 + x17*x32 + x17*x33 + x17*x35 + x17*x38 + x17*x39 + x17 + x18*x19 + x18*x23 + x18*x24 + x18*x26 + x18*x27 + x18*x34 + x18*x36 + x18*x39 + x19*x20 + x19*x22 + x19*x23 + x19*x25 + x19*x27 + x19*x28 + x19*x29 + x19*x31 + x19*x32 + x19*x35 + x19*x36 + x19*x38 + x19*x39 + x20*x21 + x20*x24 + x20*x30 + x20*x31 + x20*x32 + x20*x34 + x20*x36 + x20*x37 + x20*x38 + x20*x39 + x21*x24 + x21*x26 + x21*x27 + x21*x28 + x21*x29 + x21*x31 + x21*x34 + x21*x35 + x21*x36 + x21*x38 + x21*x39 + x21 + x22*x28 + x22*x30 + x22*x31 + x22*x32 + x22*x33 + x22*x37 + x22*x39 + x22 + x23*x30 + x23*x34 + x23*x35 + x23*x39 + x24*x26 + x24*x29 + x24*x32 + x24*x34 + x24 + x25*x26 + x25*x29 + x25*x31 + x25*x33 + x25*x36 + x25*x37 + x25*x38 + x25*x39 + x25 + x26*x27 + x26*x30 + x26*x31 + x26*x32 + x26*x34 + x26*x36 + x26*x37 + x26*x38 + x26*x39 + x26 + x27*x28 + x27*x31 + x27*x32 + x27*x33 + x27*x34 + x27*x36 + x27*x38 + x27 + x28*x29 + x28*x31 + x28*x33 + x28*x34 + x28*x35 + x28*x36 + x28*x38 + x29*x31 + x29*x34 + x29*x35 + x29*x36 + x29*x37 + x29*x39 + x29 + x30*x31 + x30*x34 + x30*x37 + x30*x38 + x30*x39 + x31*x32 + x31*x33 + x31*x34 + x31*x35 + x31*x36 + x31*x39 + x31 + x32*x34 + x32*x35 + x32*x37 + x32*x39 + x33*x35 + x33*x36 + x33*x37 + x33*x39 + x34*x35 + x34*x36 + x34*x37 + x35*x37 + x36*x37 + x36*x39 + x36 + x37*x38 + x37*x39 + x39 + 1
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x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38,x39
# planted solution: (0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1)
x0*x1 + x0*x2 + x0*x4 + x0*x5 + x0*x8 + x0*x9 + x0*x10 + x0*x11 + x0*x12 + x0*x13 + x0*x14 + x0*x15 + x0*x17 + x0*x19 + x0*x20 + x0*x27 + x0*x28 + x0*x29 + x0*x31 + x0*x36 + x0*x37 + x0 + x1*x2 + x1*x3 + x1*x5 + x1*x8 + x1*x12 + x1*x13 + x1*x18 + x1*x19 + x1*x22 + x1*x25 + x1*x27 + x1*x28 + x1*x32 + x1*x33 + x1*x34 + x1*x35 + x2*x4 + x2*x8 + x2*x12 + x2*x13 + x2*x14 + x2*x15 + x2*x17 + x2*x19 + x2*x22 + x2*x23 + x2*x25 + x2*x26 + x2*x27 + x2*x29 + x2*x30 + x2*x32 + x2*x35 + x3*x7 + x3*x9 + x3*x10 + x3*x11 + x3*x12 + x3*x13 + x3*x15 + x3*x16 + x3*x19 + x3*x22 + x3*x24 + x3*x26 + x3*x27 + x3*x30 + x3*x31 + x3*x32 + x3*x35 + x3*x38 + x3*x39 + x3 + x4*x6 + x4*x10 + x4*x11 + x4*x13 + x4*x17 + x4*x18 + x4*x20 + x4*x21 + x4*x22 + x4*x23 + x4*x24 + x4*x28 + x4*x29 + x4*x31 + x4*x32 + x4*x33 + x4*x34 + x4*x35 + x4*x39 + x5*x8 + x5*x9 + x5*x12 + x5*x13 + x5*x14 + x5*x16 + x5*x18 + x5*x20 + x5*x23 + x5*x25 + x5*x26 + x5*x28 + x5*x29 + x5*x33 + x5*x35 + x5*x36 + x5*x38 + x6*x7 + x6*x8 + x6*x9 + x6*x11 + x6*x13 + x6*x15 + x6*x17 + x6*x18 + x6*x19 + x6*x20 + x6*x23 + x6*x25 + x6*x27 + x6*x28 + x6*x29 + x6*x34 + x6*x35 + x6*x37 + x6*x38 + x7*x9 + x7*x10 + x7*x11 + x7*x13 + x7*x15 + x7*x16 + x7*x17 + x7*x23 + x7*x24 + x7*x30 + x7*x32 + x7*x35 + x7*x36 + x7*x38 + x7*x39 + x7 + x8*x18 + x8*x19 + x8*x21 + x8*x22 + x8*x23 + x8*x25 + x8*x34 + x8*x35 + x8*x38 + x8*x39 + x9*x10 + x9*x11 + x9*x12 + x9*x13 + x9*x14 + x9*x15 + x9*x16 + x9*x17 + x9*x18 + x9*x19 + x9*x25 + x9*x26 + x9*x31 + x9*x33 + x9*x38 + x9*x39 + x9 + x10*x23 + x10*x24 + x10*x25 + x10*x26 + x10*x29 + x10*x30 + x10*x31 + x10*x34 + x10*x39 + x10 + x11*x12 + x11*x14 + x11*x16 + x11*x18 + x11*x19 + x11*x21 + x11*x24 + x11*x27 + x11*x32 + x11*x33 + x11*x34 + x11*x35 + x11*x36 + x11*x37 + x11*x39 + x11 + x12*x13 + x12*x15 + x12*x16 + x12*x18 + x12*x20 + x12*x23 + x12*x25 + x12*x28 + x12*x31 + x12*x32 + x12*x35 + x12*x37 + x12*x38 + x12 + x13*x14 + x13*x19 + x13*x20 + x13*x23 + x13*x26 + x13*x30 + x13*x31 + x13*x32 + x13*x36 + x13*x37 + x13*x39 + x13 + x14*x15 + x14*x16 + x14*x17 + x14*x18 + x14*x19 + x14*x20 + x14*x23 + x14*x24 + x14*x26 + x14*x30 + x14*x31 + x14*x32 + x14*x36 + x14*x37 + x14*x39 + x14 + x15*x16 + x15*x20 + x15*x21 + x15*x23 + x15*x24 + x15*x26 + x15*x28 + x15*x29 + x15*x30 + x15*x31 + x15*x34 + x15*x35 + x15*x36 + x15*x37 + x15*x39 + x16*x17 + x16*x19 + x16*x22 + x16*x23 + x16*x24 + x16*x27 + x16*x28 + x16*x29 + x16*x32 + x16*x33 + x16*x34 + x16*x36 + x16*x37 + x16*x39 + x17*x18 + x17*x19 + x17*x21 + x17*x22 + x17*x23 + x17*x24 + x17*x26 + x17*x31 + x17*x32 + x17*x33 + x17*x34 + x17*x36 + x17*x37 + x17*x38 + x17*x39 + x18*x19 + x18*x28 + x18*x30 + x18*x32 + x18*x34 + x18*x36 + x18 + x19*x20 + x19*x22 + x19*x23 + x19*x24 + x19*x25 + x19*x27 + x19*x29 + x19*x32 + x19*x34 + x19*x35 + x19*x36 + x19*x38 + x19*x39 + x20*x23 + x20*x24 + x20*x25 + x20*x26 + x20*x28 + x20*x29 + x20*x30 + x20*x31 + x20*x32 + x20*x35 + x20*x36 + x20*x38 + x20 + x21*x22 + x21*x23 + x21*x26 + x21*x30 + x21*x35 + x21 + x22*x24 + x22*x25 + x22*x26 + x22*x30 + x22*x31 + x22*x32 + x22*x33 + x22*x35 + x22*x36 + x22*x38 + x23*x25 + x23*x26 + x23*x28 + x23*x32 + x23*x33 + x23*x35 + x23*x36 + x23*x39 + x23 + x24*x26 + x24*x30 + x24*x33 + x24*x35 + x24*x38 + x25*x26 + x25*x29 + x25*x32 + x25*x34 + x25*x37 + x25*x38 + x25*x39 + x25 + x26*x27 + x26*x28 + x26*x29 + x26*x31 + x26*x33 + x26*x34 + x26*x35 + x26*x36 + x26*x37 + x26*x38 + x26 + x27*x29 + x27*x34 + x27*x37 + x27*x38 + x27*x39 + x27 + x28*x29 + x28*x31 + x28*x32 + x28*x35 + x28*x37 + x28*x38 + x28*x39 + x28 + x29*x30 + x29*x31 + x29*x34 + x29*x35 + x29*x37 + x29*x39 + x29 + x30*x31 + x30*x33 + x30*x34 + x30*x37 + x30*x39 + x31*x32 + x31*x35 + x31*x36 + x31*x37 + x31*x39 + x31 + x32*x34 + x32*x37 + x32*x38 + x32 + x33*x34 + x33*x38 + x33*x39 + x34*x35 + x35*x36 + x35*x38 + x35 + x36*x39 + x37*x38 + x37*x39 + x37 + x38*x39 + x38 + x39 + 1
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