#include #include #include #include #include using uint = unsigned; using uint64 = unsigned long long; using namespace std; double P[11][11]; uint S[11][11]; double dp[2][2048]; double pdp[2][2048]; double ps[2048]; uint pts[2048][11]; uint trans[1 << 22][2]; uint64 s1s[2048]; uint64 s2s[2048]; const uint bits = 6; uint64 conv[1 << (3 * bits)]; int main() { uint R, C; scanf("%u %u", &R, &C); for (uint i = 0; i < R; ++i) { for (uint j = 0; j < C; ++j) { uint r; scanf("%u", &r); P[i][j] = double(r) / 100; } } for (uint i = 0; i < R; ++i) { for (uint j = 0; j < C; ++j) { scanf("%u", &S[i][j]); } } uint total = 1 << C; for (uint s = 0; s < total * total; ++s) { uint points[11] = {0}; uint plus[11] = {0}; for (uint x = 0; x < C; ++x) { points[x] = ((s >> (2 * x)) & 3) + 1; } for (uint x = 0; x < C - 1; ++x) { if (points[x] >= 4) { points[x + 1] += 1; } } for (int x = C - 1; x > 0; --x) { if (points[x] >= 4) { points[x - 1] += 1; } } uint nstate = 0; uint cnt = 0; for (uint x = 0; x < C; ++x) { if (points[x] >= 4) { nstate |= 1 << x; cnt += 1; } } trans[s][0] = nstate; trans[s][1] = cnt; } double* curr = dp[0], *next = dp[1]; double* pcurr = pdp[0], *pnext = pdp[1]; fill(curr, curr + total, .0); fill(pcurr, pcurr + total, .0); for (uint s1 = 0; s1 < total; ++s1) { uint64 t = 0; for (uint x = 0; x < C; ++x) { if (s1 & (1 << x)) { t |= 1ull << (3 * x); } } s1s[s1] = t; } for (uint s = 0; s < (1u << (3 * bits)); ++s) { uint t = s; uint c = 0; for (uint i = 0; i < bits; ++i) { int p = t & 7; c |= max(0, min(3, p - 1)) << (2 * i); t >>= 3; } conv[s] = c; } pcurr[0] = 1.0; for (uint y = 0; y < R; ++y) { fill(next, next + total, 0); fill(pnext, pnext + total, 0); for (uint s2 = 0; s2 < total; ++s2) { double p = 1.0; uint64 s = 0; for (uint x = 0; x < C; ++x) { if (s2 & (1 << x)) { p *= P[y][x]; pts[s2][x] = 4 - S[y][x]; } else { p *= 1 - P[y][x]; pts[s2][x] = 0; } s |= uint64(pts[s2][x]) << (3 * x); } ps[s2] = p; s2s[s2] = s; } for (uint s1 = 0; s1 < total; ++s1) { if (pcurr[s1] == 0) { continue; } for (uint s2 = 0; s2 < total; ++s2) { double p = ps[s2]; if (p == 0) { continue; } uint64 t = s1s[s1] + s2s[s2]; uint s = conv[t & ((1u << (3 * bits)) - 1)]; s |= conv[t >> (3 * bits)] << (2 * bits); uint nstate = trans[s][0]; uint cnt = trans[s][1]; next[nstate] += (curr[s1] + cnt * pcurr[s1]) * p; pnext[nstate] += pcurr[s1] * p; } } swap(curr, next); swap(pcurr, pnext); } double ans = 0; for (uint i = 0; i < total; ++i) { ans += curr[i]; } printf("%.12f\n", ans); return 0; }