#1120432 (C++23) No.3021 Maximize eval

提出ソース
結果

問題	No.3021 Maximize eval
コンテスト
ユーザー	ecottea
提出日時	2025-09-10 20:07:16
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	TLE
実行時間	-
コード長	35,866 bytes
コンパイル時間	16,849 ms
コンパイル使用メモリ	573,248 KB
実行使用メモリ	15,944 KB
最終ジャッジ日時	2025-09-10 20:07:40
合計ジャッジ時間	22,078 ms
ジャッジサーバーID （参考情報）	judge1 / judge2
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 1
other	AC * 1 TLE * 1 -- * 13
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ソースコード

raw source code
#ifndef HIDDEN_IN_VS // 折りたたみ用

// 警告の抑制
#define _CRT_SECURE_NO_WARNINGS

// ライブラリの読み込み
#include <bits/stdc++.h>
using namespace std;

// 型名の短縮
using ll = long long; using ull = unsigned long long; // -2^63 ～ 2^63 = 9e18（int は -2^31 ～ 2^31 = 2e9）
using pii = pair<int, int>;	using pll = pair<ll, ll>;	using pil = pair<int, ll>;	using pli = pair<ll, int>;
using vi = vector<int>;		using vvi = vector<vi>;		using vvvi = vector<vvi>;	using vvvvi = vector<vvvi>;
using vl = vector<ll>;		using vvl = vector<vl>;		using vvvl = vector<vvl>;	using vvvvl = vector<vvvl>;
using vb = vector<bool>;	using vvb = vector<vb>;		using vvvb = vector<vvb>;
using vc = vector<char>;	using vvc = vector<vc>;		using vvvc = vector<vvc>;
using vd = vector<double>;	using vvd = vector<vd>;		using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;

// 定数の定義
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左）
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;

// 入出力高速化
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;

// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順
#define repe(v, a) for(const auto& v : (a)) // a の全要素（変更不可能）
#define repea(v, a) for(auto& v : (a)) // a の全要素（変更可能）
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索（昇順）
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素（昇順）
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て（昇順）
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定

// 汎用関数の定義
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
template <class T> inline int getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod

// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }

#endif // 折りたたみ用


#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;

#ifdef _MSC_VER
#include "localACL.hpp"
#endif

using mint = modint998244353;
//using mint = static_modint<(int)1e9+7>;
//using mint = modint; // mint::set_mod(m);

using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif


#ifdef _MSC_VER // 手元環境（Visual Studio）
#include "local.hpp"
#else // 提出用（gcc）
int mute_dump = 0;
int frac_print = 0;
#if __has_include(<atcoder/all>)
namespace atcoder {
	inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
	inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
#endif
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(v)
#define dump_math(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す
#endif


//【任意文字列の列挙（置換）】O(n |cs|^n)
/*
* s[0..n) に含まれる '?' それぞれを cs の要素のいずれかに置き換えて
* 得られる文字列全てを格納したリストを返す．
*/
vector<string> enumerate_all_replace_strings(string s, const string& cs) {
	int n = sz(s);
	vector<string> strs;

	function<void(int)> rf = [&](int i) {
		if (i == n) {
			strs.push_back(s);
			return;
		}

		if (s[i] == ';') {
			char c0 = s[i];
			repe(c, cs) {
				s[i] = c;
				rf(i + 1);
			}
			s[i] = c0;
		}
		else {
			rf(i + 1);
		}
	};
	rf(0);

	return strs;
}


ll naive_sub(const string& s) {
	int n = sz(s);

	if (s[n - 1] <= '1') return -INFL;
	rep(i, n - 1) if (s[i] <= '1' && s[i + 1] <= '1') return -INFL;

	//dump(s);
	ll sum = 0, num = 0, sgn = 1;

	repe(c, s) {
		// +
		if (c == '0') {
			sum += sgn * num;
			num = 0;
			sgn = 1;
		}
		// -
		else if (c == '1') {
			sum += sgn * num;
			num = 0;
			sgn = -1;
		}
		// num
		else {
			num = num * 10 + (c - '1');
		}

		//dump(sum, mul, num);
	}
	sum += num * sgn;

	return sum;
}


#include <boost/multiprecision/cpp_int.hpp>
using Bint = boost::multiprecision::cpp_int;

using VTYPE = Bint;


// 愚直
VTYPE naive(const string& s) {
	if (s == "") return 0;

	auto ss = enumerate_all_replace_strings(s, "0123456789:");

	ll val_max = -INFL; string t_max;

	repe(t, ss) {
		auto val = naive_sub(t);
		if (chmax(val_max, val)) t_max = t;
	}

	rep(i, sz(t_max)) if (t_max[i] >= '1') t_max[i]--;

	VTYPE res = 0;
	rep(i, sz(t_max)) res = res * 10 + (t_max[i] - '0');

	return res;
}


//【行列】
/*
* Matrix<T>(int n, int m) : O(n m)
*	n×m 零行列で初期化する．
*
* Matrix<T>(int n) : O(n^2)
*	n×n 単位行列で初期化する．
*
* Matrix<T>(vvT a) : O(n m)
*	二次元配列 a[0..n)[0..m) の要素で初期化する．
*
* bool empty() : O(1)
*	行列が空かを返す．
*
* A + B : O(n m)
*	n×m 行列 A, B の和を返す．+= も使用可．
*
* A - B : O(n m)
*	n×m 行列 A, B の差を返す．-= も使用可．
*
* c * A ／ A * c : O(n m)
*	n×m 行列 A とスカラー c のスカラー積を返す．*= も使用可．
*
* A * x : O(n m)
*	n×m 行列 A と n 次元列ベクトル x の積を返す．
*
* x * A : O(n m)（やや遅い）
*	m 次元行ベクトル x と n×m 行列 A の積を返す．
*
* A * B : O(n m l)
*	n×m 行列 A と m×l 行列 B の積を返す．
*
* Mat pow(ll d) : O(n^3 log d)
*	自身を d 乗した行列を返す．
*/
template <class T>
struct Matrix {
	int n, m; // 行列のサイズ（n 行 m 列）
	vector<vector<T>> v; // 行列の成分

	// n×m 零行列で初期化する．
	Matrix(int n, int m) : n(n), m(m), v(n, vector<T>(m)) {}

	// n×n 単位行列で初期化する．
	Matrix(int n) : n(n), m(n), v(n, vector<T>(n)) { rep(i, n) v[i][i] = T(1); }

	// 二次元配列 a[0..n)[0..m) の要素で初期化する．
	Matrix(const vector<vector<T>>& a) : n(sz(a)), m(sz(a[0])), v(a) {}
	Matrix() : n(0), m(0) {}

	// 代入
	Matrix(const Matrix&) = default;
	Matrix& operator=(const Matrix&) = default;

	// アクセス
	inline vector<T> const& operator[](int i) const { return v[i]; }
	inline vector<T>& operator[](int i) {
		// verify : https://judge.yosupo.jp/problem/matrix_product

		// inline を付けて [] でアクセスするとなぜか v[] への直接アクセスより速くなった．
		return v[i];
	}

	// 入力
	friend istream& operator>>(istream& is, Matrix& a) {
		rep(i, a.n) rep(j, a.m) is >> a.v[i][j];
		return is;
	}

	// 行の追加
	void push_back(const vector<T>& a) {
		Assert(sz(a) == m);
		v.push_back(a);
		n++;
	}

	// 行の削除
	void pop_back() {
		Assert(n > 0);
		v.pop_back();
		n--;
	}

	// サイズ変更
	void resize(int n_) {
		v.resize(n_);
		n = n_;
	}

	void resize(int n_, int m_) {
		n = n_;
		m = m_;

		v.resize(n);
		rep(i, n) v[i].resize(m);
	}

	// 空か
	bool empty() const { return min(n, m) == 0; }

	// 比較
	bool operator==(const Matrix& b) const { return n == b.n && m == b.m && v == b.v; }
	bool operator!=(const Matrix& b) const { return !(*this == b); }

	// 加算，減算，スカラー倍
	Matrix& operator+=(const Matrix& b) {
		rep(i, n) rep(j, m) v[i][j] += b[i][j];
		return *this;
	}
	Matrix& operator-=(const Matrix& b) {
		rep(i, n) rep(j, m) v[i][j] -= b[i][j];
		return *this;
	}
	Matrix& operator*=(const T& c) {
		rep(i, n) rep(j, m) v[i][j] *= c;
		return *this;
	}
	Matrix operator+(const Matrix& b) const { return Matrix(*this) += b; }
	Matrix operator-(const Matrix& b) const { return Matrix(*this) -= b; }
	Matrix operator*(const T& c) const { return Matrix(*this) *= c; }
	friend Matrix operator*(const T& c, const Matrix<T>& a) { return a * c; }
	Matrix operator-() const { return Matrix(*this) *= T(-1); }

	// 行列ベクトル積 : O(m n)
	vector<T> operator*(const vector<T>& x) const {
		vector<T> y(n);
		rep(i, n) rep(j, m)	y[i] += v[i][j] * x[j];
		return y;
	}

	// ベクトル行列積 : O(m n)
	friend vector<T> operator*(const vector<T>& x, const Matrix& a) {
		vector<T> y(a.m);
		rep(i, a.n) rep(j, a.m) y[j] += x[i] * a[i][j];
		return y;
	}

	// 積：O(n^3)
	Matrix operator*(const Matrix& b) const {
		// verify : https://judge.yosupo.jp/problem/matrix_product

		Matrix res(n, b.m);
		rep(i, res.n) rep(k, m) rep(j, res.m) res[i][j] += v[i][k] * b[k][j];
		return res;
	}
	Matrix& operator*=(const Matrix& b) { *this = *this * b; return *this; }

	// 累乗：O(n^3 log d)
	Matrix pow(ll d) const {
		// verify : https://judge.yosupo.jp/problem/pow_of_matrix

		Matrix res(n), pow2 = *this;
		while (d > 0) {
			if (d & 1) res *= pow2;
			pow2 *= pow2;
			d >>= 1;
		}
		return res;
	}

#ifdef _MSC_VER
	friend ostream& operator<<(ostream& os, const Matrix& a) {
		rep(i, a.n) {
			os << "[";
			rep(j, a.m) os << a[i][j] << " ]"[j == a.m - 1];
			if (i < a.n - 1) os << "\n";
		}
		return os;
	}
#endif
};


//【転置】O(n m)
/*
* n×m 行列 A を転置した m×n 行列を返す．
*/
template <class T>
Matrix<T> transpose(const Matrix<T>& A) {
	int n = A.n, m = A.m;

	Matrix<T> AT(m, n);
	rep(i, n) rep(j, m) AT[j][i] = A[i][j];

	return AT;
}


//【単因子標準形】O(n m (n + m) log A)
/*
* A = a[0..n)[0..m) を単因子標準形 E_r := diag(e[0..r)) に変換する行列，すなわち
*		P A Q = E_r
* を満たす正則行列 P[0..n)[0..n), Q[0..m)[0..m) を求め，3 つ組 {e, P, Q} を返す．
*/
template <class T>
tuple<vector<T>, Matrix<T>, Matrix<T>> smith_normal_form(Matrix<T> A) {
	int n = A.n, m = A.m;

	auto A0(A);
	//dump("A0:"); dump(A0);

	Matrix<T> P(n), Q(m);

	rep(k, min(n, m)) {
		//dump("k:", k);

		if (A[k][k] == 0) {
			repi(i, k, n - 1) repi(j, k, m - 1) {
				if (A[i][j] != 0) {
					if (i != k) {
						swap(A[k], A[i]);
						swap(P[k], P[i]);
					}
					if (j != k) {
						rep(i2, n) swap(A[i2][k], A[i2][j]);
						rep(i2, m) swap(Q[i2][k], Q[i2][j]);
					}
					i = n;
					break;
				}
			}
		}
		//dump("A:"); dump(A);

		if (A[k][k] == 0) break;

		while (1) {
			bool updated = false;

			repi(i, k + 1, n - 1) {
				T g = gcd(A[k][k], A[i][k]);

				while (abs(A[k][k]) != g) {
					T q = A[i][k] / A[k][k];

					repi(j, k, m - 1) A[i][j] -= q * A[k][j];
					rep(j, n) P[i][j] -= q * P[k][j];

					swap(A[k], A[i]);
					swap(P[k], P[i]);

					updated = true;
				}
			}
			//dump("A:"); dump(A);

			repi(j, k + 1, m - 1) {
				T g = gcd(A[k][k], A[k][j]);
				while (abs(A[k][k]) != g) {
					T q = A[k][j] / A[k][k];

					repi(i, k, n - 1) A[i][j] -= q * A[i][k];
					rep(i, m) Q[i][j] -= q * Q[i][k];

					rep(i, n) swap(A[i][k], A[i][j]);
					rep(i, m) swap(Q[i][k], Q[i][j]);

					updated = true;
				}
			}
			//dump("A:"); dump(A);

			if (!updated) break;
		}

		repi(i, k + 1, n - 1) {
			if (A[i][k] == 0) continue;
			T q = A[i][k] / A[k][k];
			repi(j, k, m - 1) A[i][j] -= q * A[k][j];
			rep(j, n) P[i][j] -= q * P[k][j];
		}

		repi(j, k + 1, m - 1) {
			if (A[k][j] == 0) continue;
			T q = A[k][j] / A[k][k];
			repi(i, k, n - 1) A[i][j] -= q * A[i][k];
			rep(i, m) Q[i][j] -= q * Q[i][k];
		}
		//dump("A:"); dump(A);
	}

	dump("A:"); dump(A);
	if (A != P * A0 * Q) {
		dump("P:"); dump(P);
		dump("A0:"); dump(A0);
		dump("Q:"); dump(Q);
		dump("P * A0 * Q:"); dump(P* A0* Q);
		dump("A:"); dump(A);
		exit(-1);
	}

	vector<T> e;
	rep(i, min(n, m)) {
		if (A[i][i] == 0) break;
		e.push_back(A[i][i]);
	}

	return { e, P, Q };
}


auto seed = 1757501359;// time(0);
mt19937_64 mt(time(0));


// 遷移行列の係数を計算し，埋め込み用のコードを出力する．
void embed_coefs(int COL, int len_max, int L_max, int loop_cnt,
	const vector<string>& ssT_ini = { "" }, const vector<string>& ssB_ini = { "" }) {
	uniform_int_distribution<int> rnd_len(1, len_max);
	uniform_int_distribution<int> rnd_col(0, 4); // COL - 1
	uniform_int_distribution<int> rnd(0, INF);

	dump("seed:", seed);

	vector<string> ssT(ssT_ini), ssB(ssB_ini);

	// 候補とする文字列をランダムに L_max 個追加する．
	rep(hoge, L_max) {
		int len = rnd_len(mt);
		string s;
		rep(fuga, len) {
			auto tmp = rnd_col(mt);
			if (tmp == 4) tmp = COL - 1;
			s += '0' + tmp;
		}
		ssT.push_back(s);
	}
	rep(hoge, L_max / 2) {
		int len = rnd_len(mt);
		string s;
		rep(fuga, len) {
			auto tmp = rnd_col(mt);
			if (tmp == 4) tmp = COL - 1;
			s += '0' + tmp;
		}
		ssB.push_back(s);
	}

	uniq(ssT);
	uniq(ssB);
	//dump(ssT); dump(ssB);

	int LT = sz(ssT);
	int LB = sz(ssB);
	dump("LT:", LT, "LB:", LB);

	// (i,j) 成分が naive(ss[i] + ss[j]) であるような行列 mat を得る．
	Matrix<VTYPE> mat(LT, LB);
	rep(i, LT) rep(j, LB) mat[i][j] = naive(ssT[i] + ssB[j]);
	//dump("mat:"); dump(mat);

	// mat に対して行基本変形を行いピボット位置のリスト piv を得る．
	auto [e, P, Q] = smith_normal_form(mat);
	dump("e:"); dump(e);
	int RANK = sz(e);
	if (RANK < 6) exit(-1);
	//dump("P:"); dump(P);
	//dump("Q:"); dump(Q);

	// 各文字に対応する表現行列を得る．
	vector<Matrix<VTYPE>> matAs(COL, Matrix<VTYPE>(LT, LB));
	repir(c, COL - 1, 0) {
		char ch = '0' + c;
		rep(i, LT) rep(j, LB) matAs[c][i][j] = naive(ssT[i] + ch + ssB[j]);

		matAs[c] = matAs[c] * Q;
		//dump("matAs"); dump(matAs[c]);
		rep(i, LT) rep(j, RANK) {
			if (matAs[c][i][j] % e[j] != 0) {
				dump(c, i, j, ":", matAs[c][i][j], e[j]);
				exit(-1);
			}
			matAs[c][i][j] /= e[j];
		}
		matAs[c].resize(LT, LT);
		//dump("matAs"); dump(matAs[c]);
		matAs[c] = matAs[c] * P;
		//dump("matAs"); dump(matAs[c]);
	}

	// 右端を閉じるためのベクトルを得る．
	vector<VTYPE> vecP(LT);
	rep(i, LT) vecP[i] = mat[i][0];
				
	// 埋め込み用の文字列を出力する．
	string eb = "constexpr int DIM = ";
	eb += to_string(LT);
	eb += ";\n";
	eb += "constexpr int COL = ";
	eb += to_string(COL);
	eb += ";\n";
	eb += "VTYPE matAs[COL][DIM][DIM] = {\n";
	rep(c, COL) {
		eb += "{";
		rep(i, LT) {
			eb += "{";
			rep(j, LT) eb += matAs[c][i][j].str() + ",";
			eb.pop_back();
			eb += "},";
		}
		eb.pop_back();
		eb += "},\n";
	}
	eb.pop_back();
	eb.pop_back();
	eb += "};\n";
	eb += "VTYPE vecP[DIM] = {";
	rep(i, LT) eb += vecP[i].str() + ",";
	eb.pop_back();
	eb += "};\n";
	cout << eb;

	exit(0);
}


//【正方行列（固定サイズ）】
/*
* Fixed_matrix<T, n>() : O(n^2)
*	T の要素を成分にもつ n×n 零行列で初期化する．
*
* Fixed_matrix<T, n>(bool identity = true) : O(n^2)
*	T の要素を成分にもつ n×n 単位行列で初期化する．
*
* Fixed_matrix<T, n>(vvT a) : O(n^2)
*	二次元配列 a[0..n)[0..n) の要素で初期化する．
*
* A + B : O(n^2)
*	n×n 行列 A, B の和を返す．+= も使用可．
*
* A - B : O(n^2)
*	n×n 行列 A, B の差を返す．-= も使用可．
*
* c * A ／ A * c : O(n^2)
*	n×n 行列 A とスカラー c のスカラー積を返す．*= も使用可．
*
* A * x : O(n^2)
*	n×n 行列 A と n 次元列ベクトル array<T, n> x の積を返す．
*
* x * A : O(n^2)（やや遅い）
*	n 次元行ベクトル array<T, n> x と n×n 行列 A の積を返す．
*
* A * B : O(n^3)
*	n×n 行列 A と n×n 行列 B の積を返す．
*
* Mat pow(ll d) : O(n^3 log d)
*	自身を d 乗した行列を返す．
*/
template <class T, int n>
struct Fixed_matrix {
	array<array<T, n>, n> v; // 行列の成分

	// n×n 零行列で初期化する．identity = true なら n×n 単位行列で初期化する．
	Fixed_matrix(bool identity = false) {
		rep(i, n) v[i].fill(T(0));
		if (identity) rep(i, n) v[i][i] = T(1);
	}

	// 二次元配列 a[0..n)[0..n) の要素で初期化する．
	Fixed_matrix(const vector<vector<T>>& a) {
		// verify : https://yukicoder.me/problems/no/1000

		Assert(sz(a) == n && sz(a[0]) == n);
		rep(i, n) rep(j, n) v[i][j] = a[i][j];
	}

	// 代入
	Fixed_matrix(const Fixed_matrix&) = default;
	Fixed_matrix& operator=(const Fixed_matrix&) = default;

	// アクセス
	inline array<T, n> const& operator[](int i) const { return v[i]; }
	inline array<T, n>& operator[](int i) { return v[i]; }

	// 入力
	friend istream& operator>>(istream& is, Fixed_matrix& a) {
		rep(i, n) rep(j, n) is >> a[i][j];
		return is;
	}

	// 比較
	bool operator==(const Fixed_matrix& b) const { return v == b.v; }
	bool operator!=(const Fixed_matrix& b) const { return !(*this == b); }

	// 加算，減算，スカラー倍
	Fixed_matrix& operator+=(const Fixed_matrix& b) {
		rep(i, n) rep(j, n) v[i][j] += b[i][j];
		return *this;
	}
	Fixed_matrix& operator-=(const Fixed_matrix& b) {
		rep(i, n) rep(j, n) v[i][j] -= b[i][j];
		return *this;
	}
	Fixed_matrix& operator*=(const T& c) {
		rep(i, n) rep(j, n) v[i][j] *= c;
		return *this;
	}
	Fixed_matrix operator+(const Fixed_matrix& b) const { return Fixed_matrix(*this) += b; }
	Fixed_matrix operator-(const Fixed_matrix& b) const { return Fixed_matrix(*this) -= b; }
	Fixed_matrix operator*(const T& c) const { return Fixed_matrix(*this) *= c; }
	friend Fixed_matrix operator*(const T& c, const Fixed_matrix& a) { return a * c; }
	Fixed_matrix operator-() const { return Fixed_matrix(*this) *= T(-1); }

	// 行列ベクトル積 : O(n^2)
	array<T, n> operator*(const array<T, n>& x) const {
		array<T, n> y{ 0 };
		rep(i, n) rep(j, n)	y[i] += v[i][j] * x[j];
		return y;
	}

	// ベクトル行列積 : O(n^2)
	friend array<T, n> operator*(const array<T, n>& x, const Fixed_matrix& a) {
		array<T, n> y{ 0 };
		rep(i, n) rep(j, n) y[j] += x[i] * a[i][j];
		return y;
	}

	// 積：O(n^3)
	Fixed_matrix operator*(const Fixed_matrix& b) const {
		// verify : https://yukicoder.me/problems/no/1000

		Fixed_matrix res;
		rep(i, n) rep(k, n) rep(j, n) res[i][j] += v[i][k] * b[k][j];
		return res;
	}
	Fixed_matrix& operator*=(const Fixed_matrix& b) { *this = *this * b; return *this; }

	// 累乗：O(n^3 log d)
	Fixed_matrix pow(ll d) const {
		// verify : https://yukicoder.me/problems/no/2810

		Fixed_matrix res(true), pow2(*this);
		while (d > 0) {
			if (d & 1) res *= pow2;
			pow2 *= pow2;
			d /= 2;
		}
		return res;
	}

#ifdef _MSC_VER
	friend ostream& operator<<(ostream& os, const Fixed_matrix& a) {
		rep(i, n) {
			os << "[";
			rep(j, n) os << a[i][j] << " ]"[j == n - 1];
			if (i < n - 1) os << "\n";
		}
		return os;
	}
#endif
}; 


template <class VTYPE>
VTYPE solve(const string& s) {
	// --------------- embed_coefs() からの出力を貼る ----------------
	constexpr int DIM = 22;
	constexpr int COL = 12;
	int matAs[COL][DIM][DIM] = {
	{{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,1,0,210,0,0,0,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1800,1,0,1890,0,0,0,0,-90,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,1,0,210,0,0,0,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0},{-4200,1,0,4410,0,0,0,0,-210,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2200,1,0,2310,0,0,0,0,-110,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,1,0,210,0,0,0,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0},{-20200,1,0,21210,0,0,0,0,-1010,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2400,1,0,2520,0,0,0,0,-120,0,0,0,0,0,0,0,0,0,0,0,0,0},{-3800,1,0,3990,0,0,0,0,-190,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-400,1,0,420,0,0,0,0,-20,0,0,0,0,0,0,0,0,0,0,0,0,0},{-42400,1,0,44520,0,0,0,0,-2120,0,0,0,0,0,0,0,0,0,0,0,0,0},{-4400,1,0,4620,0,0,0,0,-220,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1800,1,0,1890,0,0,0,0,-90,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-18400,1,0,19320,0,0,0,0,-920,0,0,0,0,0,0,0,0,0,0,0,0,0}},
	{{0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,0,0,210,0,0,1,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1800,0,0,1890,0,0,1,0,-90,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,0,0,210,0,0,1,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0},{-4200,0,0,4410,0,0,1,0,-210,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2200,0,0,2310,0,0,1,0,-110,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,0,0,210,0,0,1,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0},{-20200,0,0,21210,0,0,1,0,-1010,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2400,0,0,2520,0,0,1,0,-120,0,0,0,0,0,0,0,0,0,0,0,0,0},{-3800,0,0,3990,0,0,1,0,-190,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-400,0,0,420,0,0,1,0,-20,0,0,0,0,0,0,0,0,0,0,0,0,0},{-42400,0,0,44520,0,0,1,0,-2120,0,0,0,0,0,0,0,0,0,0,0,0,0},{-4400,0,0,4620,0,0,1,0,-220,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1800,0,0,1890,0,0,1,0,-90,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-18400,0,0,19320,0,0,1,0,-920,0,0,0,0,0,0,0,0,0,0,0,0,0}},
	{{0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-10,0,0,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,0,0,200,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-90,0,0,91,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-10,0,0,10,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,0,0,201,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-100,0,0,101,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-10,0,0,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1010,0,0,1010,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-120,0,0,121,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-190,0,0,191,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1900,0,0,1901,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-20,0,0,21,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2120,0,0,2121,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-220,0,0,221,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2200,0,0,2201,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-90,0,0,91,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-900,0,0,901,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-920,0,0,921,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},
	{{-1,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-11,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-201,0,0,201,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-91,0,0,92,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-11,0,0,11,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-201,0,0,202,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-101,0,0,102,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-11,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1011,0,0,1011,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-121,0,0,122,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-191,0,0,192,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1901,0,0,1902,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-21,0,0,22,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2121,0,0,2122,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-221,0,0,222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2201,0,0,2202,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-91,0,0,92,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-901,0,0,902,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-921,0,0,922,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},
	{{-2,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-12,0,0,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-202,0,0,202,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-92,0,0,93,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2,0,0,2,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-12,0,0,12,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-202,0,0,203,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-102,0,0,103,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-12,0,0,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1012,0,0,1012,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-122,0,0,123,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-192,0,0,193,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1902,0,0,1903,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-22,0,0,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2122,0,0,2123,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-222,0,0,223,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2202,0,0,2203,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-92,0,0,93,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-902,0,0,903,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-922,0,0,923,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},
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	{{-7,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-7,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-17,0,0,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-207,0,0,207,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-97,0,0,98,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-7,0,0,7,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-17,0,0,17,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-207,0,0,208,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-107,0,0,108,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-17,0,0,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1017,0,0,1017,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-127,0,0,128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-197,0,0,198,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1907,0,0,1908,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-27,0,0,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2127,0,0,2128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-227,0,0,228,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2207,0,0,2208,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-97,0,0,98,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-907,0,0,908,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-927,0,0,928,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},
	{{-8,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-8,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-18,0,0,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-208,0,0,208,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-98,0,0,99,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-8,0,0,8,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-18,0,0,18,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-208,0,0,209,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-108,0,0,109,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-18,0,0,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1018,0,0,1018,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-128,0,0,129,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-198,0,0,199,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1908,0,0,1909,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-28,0,0,29,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2128,0,0,2129,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-228,0,0,229,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2208,0,0,2209,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-98,0,0,99,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-908,0,0,909,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-928,0,0,929,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},
	{{-8,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-8,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-18,0,0,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-200,0,0,200,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-98,0,0,99,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{10,0,0,-10,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{-208,0,0,209,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-108,0,0,109,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-18,0,0,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-990,0,0,990,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{-128,0,0,129,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-198,0,0,199,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1908,0,0,1909,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-28,0,0,29,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2128,0,0,2129,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-228,0,0,229,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-2208,0,0,2209,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-98,0,0,99,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-908,0,0,909,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-928,0,0,929,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}} };
	int vecP[DIM] = { 0,0,0,1,0,9,0,1,21,11,1,101,12,19,0,2,212,22,0,9,0,92 };
	// --------------------------------------------------------------

	array<Fixed_matrix<VTYPE, DIM>, COL> MatAs;
	rep(k, COL) rep(i, DIM) rep(j, DIM) MatAs[k][i][j] = matAs[k][i][j];

	array<VTYPE, DIM> VecP;
	rep(i, DIM) VecP[i] = vecP[i];

	int n = sz(s);

	vector<Fixed_matrix<VTYPE, DIM>> a(n);
	rep(p, n) a[p] = MatAs[s[p] - '0'];

	// 2 冪個ずつ掛けていく（分割統治法）
	for (int k = 1; k < n; k *= 2) {
		for (int i = 0; i + k < n; i += 2 * k) {
			a[i] = a[i] * a[i + k];
		}
	}

	return (a[0] * VecP)[0];
}


int main() {
	input_from_file("input.txt");
//	output_to_file("output.txt");

	//【方法】
	// 愚直を書いて集めたデータをもとに遷移行列を復元する．

	//【使い方】
	// 1. mint naive(文字列) を実装する．
	// 2. embed_coefs(文字の種類数); を実行する．
	// 3. 出力を solve() 内に貼る．
	// 4. auto dp = solve<答えの型>(文字列) で勝手に DP してくれる．
	
	dump("naive:", naive("1212")); dump("=====");

	vector<string> ssT_ini{ "" }, ssB_ini{ "" };
		
	// (文字の種類数，長さの最大値，1回で追加する文字列の量，反復回数)
//	embed_coefs(12, 3, 20, 1, ssT_ini, ssB_ini);

	int T;
	cin >> T;

	rep(hoge, T) {
		string s;
		cin >> s;

		rep(i, sz(s)) {
			if (s[i] == '+') s[i] = '0';
			else if (s[i] == '-') s[i] = '1';
			else if (s[i] == '?') s[i] = ';';
			else s[i] = s[i] + 1;
		}

		dump("naive:", naive(s)); dump("=====");

		auto res = solve<Bint>(s).str();
		if (sz(res) != sz(s)) res.insert(res.begin(), '0');
		rep(i, sz(s)) {
			if (res[i] == '0') {
				if (s[i] == '1') res[i] = '-';
				else res[i] = '+';
			}
		}

		cout << res << "\n"; // TLE．行列がでかすぎ
	}
}