#include "abc.h"
#include <cstring>
const int N = 30;
const int M = 1000;
const int L = 16;
const int LN = 5; /* LN = ceil(log2(N)) */
const int OP_INPUT = -1;
const int OP_ZERO = 0; // f(OP_ZERO, x0, x1) = 0
const int OP_NOR = 1; // f(OP_NOR, x0, x1) = !(x0 || x1)
const int OP_GREATER = 2; // f(OP_GREATER, x0, x1) = (x0 > x1)
const int OP_NOT_X1 = 3; // f(OP_NOT_X1, x0, x1) = !x1
const int OP_LESS = 4; // f(OP_LESS, x0, x1) = (x0 < x1)
const int OP_NOT_X0 = 5; // f(OP_NOT_X0, x0, x1) = !x0
const int OP_XOR = 6; // f(OP_XOR, x0, x1) = (x0 ^ x1)
const int OP_NAND = 7; // f(OP_NAND, x0, x1) = !(x0 && x1)
const int OP_AND = 8; // f(OP_AND, x0, x1) = (x0 && x1)
const int OP_EQUAL = 9; // f(OP_EQUAL, x0, x1) = (x0 == x1)
const int OP_X0 = 10; // f(OP_X0, x0, x1) = x0
const int OP_GEQ = 11; // f(OP_GEQ, x0, x1) = (x0 >= x1)
const int OP_X1 = 12; // f(OP_X1, x0, x1) = x1
const int OP_LEQ = 13; // f(OP_LEQ, x0, x1) = (x0 <= x1)
const int OP_OR = 14; // f(OP_OR, x0, x1) = (x0 || x1)
const int OP_ONE = 15; // f(OP_ONE, x0, x1) = 1
#define OPS op, uu, k
unsigned int AX;
int alice_rand() {
return (AX *= 3) >> 1;
}
void alice_sort(const char name[][5], int *ii, int l, int r) {
while (l < r) {
int i = l, j = l, k = r, i_ = ii[l + alice_rand() % (r - l)], tmp;
while (j < k) {
int c = strcmp(name[ii[j]], name[i_]);
if (c == 0)
j++;
else if (c < 0) {
tmp = ii[i], ii[i] = ii[j], ii[j] = tmp;
i++, j++;
} else {
k--;
tmp = ii[j], ii[j] = ii[k], ii[k] = tmp;
}
}
alice_sort(name, ii, l, i);
l = k;
}
}
int alice(const int n, const char name[][5], const unsigned short xx[], bool aa[]) {
if (n == 1) {
for (int h = 0; h < L; h++)
aa[h] = xx[0] >> h & 1;
return L;
} else {
int ii[N];
for (int i = 0; i < n; i++)
ii[i] = i;
AX = 12345, alice_sort(name, ii, 0, n);
for (int i = 0; i < n; i++) {
for (int l = 0; l < LN; l++)
aa[i * (LN + L) + l] = ii[i] >> l & 1;
for (int l = 0; l < L; l++)
aa[i * (LN + L) + (LN + l)] = xx[ii[i]] >> l & 1;
}
return n * (LN + L);
}
}
unsigned int BX;
int bob_rand() {
return (BX *= 3) >> 1;
}
void bob_sort(const char name[][5], int *ii, int l, int r) {
while (l < r) {
int i = l, j = l, k = r, i_ = ii[l + bob_rand() % (r - l)], tmp;
while (j < k) {
int c = strcmp(name[ii[j]], name[i_]);
if (c == 0)
j++;
else if (c < 0) {
tmp = ii[i], ii[i] = ii[j], ii[j] = tmp;
i++, j++;
} else {
k--;
tmp = ii[j], ii[j] = ii[k], ii[k] = tmp;
}
}
bob_sort(name, ii, l, i);
l = k;
}
}
int bob(const int m, const char uu[][5], const char vv[][5], bool bb[]) {
for (int l = 0; l < L; l++)
bb[l] = m >> l & 1;
char name[M * 2][5];
int hh[M * 2], ii[M * 2];
for (int h = 0; h < m; h++)
strcpy(name[h << 1 | 0], uu[h]), strcpy(name[h << 1 | 1], vv[h]);
for (int h = 0; h < m * 2; h++)
hh[h] = h;
BX = 12345, bob_sort(name, hh, 0, m * 2);
int n = 0;
for (int h = 0; h < m * 2; h++)
ii[hh[h]] = h + 1 == m * 2 || strcmp(name[hh[h + 1]], name[hh[h]]) != 0 ? n++ : n;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
bb[L + i * n + j] = 0;
for (int h = 0; h < m; h++)
bb[L + ii[h << 1 | 0] * n + ii[h << 1 | 1]] = 1;
return L + n * n;
}
int gate(int op[], int uu[][2], int &k, int o, int u, int v) {
op[k] = o, uu[k][0] = u, uu[k][1] = v;
return k++;
}
void add1(int op[], int uu[][2], int &k, int *cc, int u, int i) {
for (int j = i; j < L; j++) {
int c = gate(OPS, OP_XOR, cc[j], u), v = gate(OPS, OP_AND, cc[j], u);
cc[j] = c, u = v;
}
}
void mult(int op[], int uu[][2], int &k, int *aa, int *bb, int *cc) {
for (int i = 0; i < L; i++)
for (int j = 0; i + j < L; j++)
add1(OPS, cc, gate(OPS, OP_AND, aa[i], bb[j]), i + j);
}
int circuit(const int ka, const int kb, int op[], int uu[][2], int outputs_circuit[][16]) {
int k = 0;
for (int h = 0; h < ka + kb; h++)
gate(OPS, OP_INPUT, -1, -1);
int ZERO = gate(OPS, OP_ZERO, 0, 0), ONE = gate(OPS, OP_ONE, 0, 0);
if (ka == L) {
int aa[L], bb[L], cc[L];
for (int l = 0; l < L; l++)
aa[l] = l, bb[l] = L + l;
for (int l = 0; l < L; l++)
cc[l] = ZERO;
mult(OPS, aa, bb, cc);
for (int l = 0; l < L; l++)
outputs_circuit[0][l] = cc[l];
return k;
} else {
int n = 0;
while (L + n * n < kb)
n++;
int cc[N][L];
for (int i = 0; i < n; i++)
for (int l = 0; l < L; l++)
cc[i][l] = ZERO;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
for (int l = 0; l < L; l++)
add1(OPS, cc[j], gate(OPS, OP_AND, ka + L + i * n + j, i * (LN + L) + LN + l), l);
for (int i = 0; i < n; i++)
for (int l = 0; l < L; l++)
outputs_circuit[i][l] = ZERO;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
int eq = ONE;
for (int l = 0; l < LN; l++)
eq = gate(OPS, OP_AND, eq, gate(OPS, OP_EQUAL, i * (LN + L) + l, (j & 1 << l) == 0 ? ZERO : ONE));
for (int l = 0; l < L; l++)
add1(OPS, outputs_circuit[j], gate(OPS, OP_AND, eq, cc[i][l]), l);
}
return k;
}
}
