/** @file 0792.cpp @title No.792 真理関数をつくろう - yukicoder @url https://yukicoder.me/problems/no/792 **/ #include using namespace std; typedef long long LL; typedef unsigned long long uLL; typedef unsigned int uint; #define ALL(obj) (obj).begin(), (obj).end() #define RALL(x) (x).rbegin(), (x).rend() #define SZ(x) ((int)(x).size()) #define REPI(i, a, b) for (LL i = LL(a); i < LL(b); ++i) #define REP(i, N) for (LL i = LL(0); i < LL(N); ++i) #define REPS(i, N) for (int i = 1; i <= (int)(N); i++) #define RREP(i, N) for (int i = ((int)(N)-1); i >= 0; i--) #define RREPS(i, N) for (int i = ((int)(N)); i > 0; i--) #define chmax(ret, x) ret = max(ret, x) #define chmin(ret, x) ret = min(ret, x) #define FILL(x, e) memset(x, e, sizeof(x)) #define ZEROS(x) fill(x, 0) #define SORT(x) sort(ALL(x)) #define RSORT(x) sort(RALL(x)) #define UNIQ(x) x.erase(unique(ALL(x)), x.end()) #define BIT(n) (1LL << (n)) #define OUT(x) cout << (x) << "\n" #define DEBUG(x) cerr << #x << " : " << x << "\n" #define DEBUG2(x, y) cerr << "(" << #x << ", " << #y << ") = (" << x << ", " << y << ")\n"; #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second const int MOD = 1e9 + 7; void iostream_init() { ios::sync_with_stdio(false); cin.tie(0); cout.setf(ios::fixed); cout.precision(12); // cout.fill('0'); // cout.width(3); } int main() { ::iostream_init(); int N; cin >> N; vector tmpQ(N, 0); vector> Q; vector R(pow(2, N), 0); REP(i, pow(2, N)) { REP(j, N) { cin >> tmpQ[j]; } cin >> R[i]; Q.PB(tmpQ); } string str_and = "∧"; string str_or = "∨"; string str_not = "¬"; string str_top = "⊤"; // all true string str_btm = "⊥"; // all false int c = 0; vector buf; REP(i, (int)pow(2, N)) { string tmp = ""; if (R[i] == 1) { c++; tmp += "("; REP(j, N) { if (Q[i][j] == 1) { tmp += ("P_" + to_string(j + 1)); } else { tmp += str_not; tmp += ("P_" + to_string(j + 1)); } if (j != N - 1) { tmp += str_and; } } tmp += ")"; buf.PB(tmp); } } string ans = "A="; REP(i, SZ(buf)) { ans += buf[i]; if (i != (SZ(buf) - 1)) { ans += str_or; } } if (c == pow(2, N)) { ans = "A=" + str_top; } else if (c == 0) { ans = "A=" + str_btm; } OUT(ans); return 0; }