//////////////////////////////////////// /// tu3 pro-con template /// //////////////////////////////////////// #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //// MACRO //// #define countof(a) (sizeof(a)/sizeof(a[0])) #define REP(i,n) for (int i = 0; i < (n); i++) #define RREP(i,n) for (int i = (n)-1; i >= 0; i--) #define FOR(i,s,n) for (int i = (s); i < (n); i++) #define RFOR(i,s,n) for (int i = (n)-1; i >= (s); i--) #define pos(c,i) c.being() + (i) #define allof(c) c.begin(), c.end() #define aallof(a) a, countof(a) #define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n) #define apartof(a,i,n) a + (i), a + (i) + (n) typedef unsigned int uint; typedef long long llong; typedef unsigned long long ullong; #define long long long #define EPS 1e-9 #define INF (1L << 28) #define LINF (1LL << 60) #define PREDICATE(t,a,exp) [&](const t & a) -> bool { return exp; } #define COMPARISON_T(t) bool(*)(const t &, const t &) #define COMPARISON(t,a,b,exp) [&](const t & a, const t & b) -> bool { return exp; } #define CONVERTER(TSrc,t,TDest,exp) [&](const TSrc &t)->TDest { return exp; } inline int sign_of(double x) { return abs(x) < EPS ? 0 : x > 0 ? 1 : -1; } inline bool inRange(int val, int min, int max) { return val >= min && val < max; } inline bool inRange(double val, double min, double max) { return val - min > -EPS && val - max < EPS; } inline bool inRange(int x, int y, int W, int H) { return x >= 0 && x < W && y >= 0 && y < H; } // W,H含まない template struct vevector : public vector> { vevector(int n = 0, int m = 0, const T &initial = T()) : vector>(n, vector(m, initial)) { } }; template struct vevevector : public vector> { vevevector(int n = 0, int m = 0, int l = 0, const T &initial = T()) : vector>(n, vevector(m, l, initial)) { } }; template struct vevevevector : public vector> { vevevevector(int n = 0, int m = 0, int l = 0, int k = 0, const T &initial = T()) : vector>(n, vevevector(m, l, k, initial)) { } }; //// i/o helper //// namespace std { template inline istream & operator >> (istream & in, pair &p) { in >> p.first >> p.second; return in; } template inline ostream & operator << (ostream &out, const pair &p) { out << p.first << " " << p.second; return out; } } template T read() { T t; cin >> t; return t; } template vector read(int n) { vector v; v.reserve(n); REP(i, n) { v.push_back(read()); } return v; } template vevector read(int n, int m) { vevector v; REP(i, n) v.push_back(read(m)); return v; } template vector readjag() { return read(read()); } template vevector readjag(int n) { vevector v; v.reserve(n); REP(i, n) v.push_back(readjag()); return v; } template struct iter_pair_t { T beg, end; }; template iter_pair_t iter_pair(T beg, T end) { return iter_pair_t{beg, end}; } template ostream & operator << (ostream &out, const iter_pair_t &v) { std::copy(v.beg, v.end, ostream_iterator(out, " ")); return out; } template ostream & operator << (ostream &out, const vector &v) { return out << iter_pair(begin(v), end(v)); } template ostream & operator << (ostream &out, const set &v) { return out << iter_pair(begin(v), end(v)); } template ostream & operator << (ostream &out, const map &v) { return out << iter_pair(begin(v), end(v)); } struct _Reader { istream &cin; template _Reader operator ,(T &rhs) { cin >> rhs; return *this; } }; struct _Writer { ostream &cout; bool f{ false }; template _Writer operator ,(const T &rhs) { cout << (f ? " " : "") << rhs; f = true; return *this; } }; #define READ(t,...) t __VA_ARGS__; (_Reader{cin}), __VA_ARGS__ #define WRITE(...) (_Writer{cout}), __VA_ARGS__; cout << '\n' #define DEBUG(...) (_Writer{cerr}), __VA_ARGS__; cerr << '\n' void solve(); int main() { cin.tie(0); ios_base::sync_with_stdio(false); cout << setprecision(std::numeric_limits::max_digits10); solve(); return 0; } enum struct GaussJordanResult { One, Inconsistent, Ambiguous, }; GaussJordanResult gaussJordan(vevector &m) { int R = m.size(); int C = m[0].size() - 1; int pi = 0; REP(pj, C) { // ピボット選択 FOR(i, pi + 1, R) { if (abs(m[i][pj]) > abs(m[pi][pj])) { m[pi].swap(m[i]); } } if (m[pi][pj]) { { double r = m[pi][pj]; REP(j, C + 1) { m[pi][j] /= r; } } REP(i, R) { if (i == pi) { continue; } double r = m[i][pj]; REP(j, C + 1) { m[i][j] = m[i][j] - r * m[pi][j]; } } pi++; } } { // 0 = !0 のような式が残ってると解なし。 FOR(i, pi, R) { if (abs(m[i][C]) > EPS) { return GaussJordanResult::Inconsistent; } } return pi == C ? GaussJordanResult::One : GaussJordanResult::Ambiguous; } } template vector gaussJordanAns(const vevector &m) { // 行列のランクが列数より低い → 解が一意に定まらない // 1 d 0 | a // 0 0 1 | b のようなときは、x[0] = a, x[1] = 0, x[2] = b が解の1つ // 0 0 0 | 0 int C = m[0].size() - 1; vector ans(C); int i = 0; REP(j, C) { while (abs(m[i][j]) < EPS) { j++; } ans[j] = m[i][C]; i++; } return ans; } //////////////////// /// template end /// //////////////////// void solve() { READ(int, N); auto A = read(N); vevector m(N, N + 1, 1); REP(i, N) { m[i][i] = 0; m[i][N] = A[i]; } auto r = gaussJordan(m); if (r == GaussJordanResult::One) { map ma; for(auto d : gaussJordanAns(m)) { ma[int(d + EPS)]++; } WRITE(ma[2], ma[4]); } else { throw r; } }