#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)x.size()
#define beg(x) x.begin()
#define en(x) x.end()
#define all(x) beg(x), en(x)
#define resz resize
const int MOD = 1000000007; // 998244353
const ll INF = 1e18;
const int MX = 100001;
const ld PI = 4*atan((ld)1);
template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }
namespace input {
template<class T> void re(complex<T>& x);
template<class T1, class T2> void re(pair<T1,T2>& p);
template<class T> void re(vector<T>& a);
template<class T, size_t SZ> void re(array<T,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(double& x) { string t; re(t); x = stod(t); }
void re(ld& x) { string t; re(t); x = stold(t); }
template<class Arg, class... Args> void re(Arg& first, Args&... rest) {
re(first); re(rest...);
}
template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}
using namespace input;
namespace output {
template<class T1, class T2> void pr(const pair<T1,T2>& x);
template<class T, size_t SZ> void pr(const array<T,SZ>& x);
template<class T> void pr(const vector<T>& x);
template<class T> void pr(const set<T>& x);
template<class T1, class T2> void pr(const map<T1,T2>& x);
template<class T> void pr(const T& x) { cout << x; }
template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) {
pr(first); pr(rest...);
}
template<class T1, class T2> void pr(const pair<T1,T2>& x) {
pr("{",x.f,", ",x.s,"}");
}
template<class T> void prContain(const T& x) {
pr("{");
bool fst = 1; trav(a,x) pr(!fst?", ":"",a), fst = 0;
pr("}");
}
template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
template<class T> void pr(const vector<T>& x) { prContain(x); }
template<class T> void pr(const set<T>& x) { prContain(x); }
template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }
void ps() { pr("\n"); }
template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) {
pr(first," "); ps(rest...); // print w/ spaces
}
}
using namespace output;
namespace io {
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void setIO(string s = "") {
ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
}
using namespace io;
template<class T> T invGeneral(T a, T b) {
a %= b; if (a == 0) return b == 1 ? 0 : -1;
T x = invGeneral(b,a);
return x == -1 ? -1 : ((1-(ll)b*x)/a+b)%b;
}
template<class T> struct modular {
T val;
explicit operator T() const { return val; }
modular() { val = 0; }
template<class U> modular(const U& v) {
val = (-MOD <= v && v <= MOD) ? v : v % MOD;
if (val < 0) val += MOD;
}
friend ostream& operator<<(ostream& os, const modular& a) { return os << a.val; }
friend bool operator==(const modular& a, const modular& b) { return a.val == b.val; }
friend bool operator!=(const modular& a, const modular& b) { return !(a == b); }
modular operator-() const { return modular(-val); }
modular& operator+=(const modular& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; }
modular& operator-=(const modular& m) { if ((val -= m.val) < 0) val += MOD; return *this; }
modular& operator*=(const modular& m) { val = (ll)val*m.val%MOD; return *this; }
friend modular exp(modular a, ll p) {
modular ans = 1; for (; p; p /= 2, a *= a) if (p&1) ans *= a;
return ans;
}
friend modular inv(const modular& a) { return invGeneral(a.val,MOD); }
// inv is equivalent to return exp(b,b.mod-2) if prime
modular& operator/=(const modular& m) { return (*this) *= inv(m); }
friend modular operator+(modular a, const modular& b) { return a += b; }
friend modular operator-(modular a, const modular& b) { return a -= b; }
friend modular operator*(modular a, const modular& b) { return a *= b; }
friend modular operator/(modular a, const modular& b) { return a /= b; }
};
typedef modular<int> mi;
typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
int N;
string S;
mi ans(0);
void tri0(int d, int t) {
// max1 <= max2-d
// all in first prefix <= max1
// need smth >= t+d in second
// 0: not yet < 0, not found t
// 1: not yet < 0, found t
// 2: < 0, but never > 2t
// if 2d-1 -> 2d maybe go to 3
// 3: not found smth >= max1+d
// 4: found smth >= max1+d
// end: =2d
array<array<mi,5>,201> cur = array<array<mi,5>,201>();
cur[N][0 >= t] = 1;
trav(c,S) {
array<array<mi,5>,201> tmp = array<array<mi,5>,201>();
FOR(i,-N,N+1) {
int e = (int)cur[N+i][0];
if (e) {
if (c != ')') tmp[N+i+1][i+1 >= t] += e;
if (c != '(' && i) tmp[N+i-1][0] += e;
}
e = (int)cur[N+i][1];
if (e) {
if (c != ')' && i+1 <= t) tmp[N+i+1][1] += e;
if (c != '(') {
assert(i >= 0);
tmp[N+i-1][1+(i == 0)] += e;
}
}
e = (int)cur[N+i][2];
if (e) {
if (c != ')') {
if (i == 2*d-1) tmp[N+i+1][3+(i+1 >= t+d)] += e;
if (i+1 <= 2*t) tmp[N+i+1][2] += e;
}
if (c != '(') tmp[N+i-1][2] += e;
}
e = (int)cur[N+i][3];
if (e) {
if (c != ')') tmp[N+i+1][3+(i+1 >= t+d)] += e;
if (c != '(' && i-1 >= 2*d) tmp[N+i-1][3] += e;
}
e = (int)cur[N+i][4];
if (e) {
if (c != ')') tmp[N+i+1][4] += e;
if (c != '(' && i-1 >= 2*d) tmp[N+i-1][4] += e;
}
}
swap(cur,tmp);
}
ans += cur[N+2*d][4];
}
void tri1(int d, int t) {
// max1 > max2-d
// need smth > t in first prefix
// all in second prefix <= t+d, need occurrence of t+d
array<array<mi,5>,201> cur = array<array<mi,5>,201>();
cur[N][0] = 1;
trav(c,S) {
array<array<mi,5>,201> tmp = array<array<mi,5>,201>();
FOR(i,-N,N+1) {
int e = (int)cur[N+i][0];
if (e) {
if (c != ')') tmp[N+i+1][i+1 > t] += e;
if (c != '(' && i) tmp[N+i-1][0] += e;
}
e = (int)cur[N+i][1];
if (e) {
if (c != ')') tmp[N+i+1][1] += e;
if (c != '(') {
assert(i >= 0);
tmp[N+i-1][1+(i == 0)] += e;
}
}
e = (int)cur[N+i][2];
if (e) {
if (c != ')') {
if (i == 2*d-1) tmp[N+i+1][3+(i+1 >= t+d)] += e;
if (i+1 <= 2*t) tmp[N+i+1][2] += e;
}
if (c != '(') tmp[N+i-1][2] += e;
}
e = (int)cur[N+i][3];
if (e) {
if (c != ')') tmp[N+i+1][3+(i+1 >= t+d)] += e;
if (c != '(' && i-1 >= 2*d) tmp[N+i-1][3] += e;
}
e = (int)cur[N+i][4];
if (e) {
if (c != ')' && i+1 <= t+d) tmp[N+i+1][4] += e;
if (c != '(' && i-1 >= 2*d) tmp[N+i-1][4] += e;
}
}
swap(cur,tmp);
}
ans += cur[N+2*d][4];
}
void balanced() {
array<mi,201> cur = array<mi,201>(); cur[0] = 1;
trav(c,S) {
array<mi,201> tmp = array<mi,201>();
F0R(i,N+1) {
int e = (int)cur[i];
if (e) {
if (c != ')') tmp[i+1] += e;
if (c != '(' && i) tmp[i-1] += e;
}
}
swap(cur,tmp);
}
// ps("??",cur[0]);
ans += cur[0];
}
void cool(int d) {
// keep track of current mx: 2*d, current sum
// 0: not found
// 1: everything must <= 2*(mx-d) until you get to mx-d
// 2: found
// csum, mx
array<array<array<mi,3>,101>,101> cur = array<array<array<mi,3>,101>,101>();
cur[2*d][2*d][0] = 1;
trav(c,S) {
array<array<array<mi,3>,101>,101> tmp = array<array<array<mi,3>,101>,101>();
F0R(i,N+1) F0R(j,N+1) {
int e = (int)cur[i][j][0];
if (e) {
if (c != ')') {
if (i+1 <= N) tmp[i+1][max(i+1,j)][0] += e;
}
if (c != '(') {
if (i-1 >= 0) {
if (j-d == i-1) tmp[i-1][j][1] += e;
else if (i-1 < 2*d) tmp[i-1][j][2] += e;
else tmp[i-1][j][0] += e;
}
}
}
e = (int)cur[i][j][1];
if (e) {
if (c != ')') {
if (i+1 <= N) tmp[i+1][j][1] += e;
}
if (c != '(') {
if (i-1 >= 0) tmp[i-1][j][1] += e;
}
}
e = (int)cur[i][j][2];
if (e) {
if (c != ')') {
if (i+1 <= min(N,2*(j-d))) tmp[i+1][j][2] += e;
}
if (c != '(') {
if (i-1 >= 0) {
if (j-d == i-1) tmp[i-1][j][1] += e;
else tmp[i-1][j][2] += e;
}
}
}
}
swap(cur,tmp);
}
F0R(i,N+1) ans += cur[0][i][1];
}
void solve(int d) {
FOR(t,d,N-d+1) {
tri0(d,t);
tri1(d,t);
}
if (d == 0) balanced();
else cool(d);
}
int main() {
setIO(); re(N,S);
if (N&1) { ps(0); exit(0); }
solve(0);
FOR(d,1,N/2+1) solve(d);
reverse(all(S));
trav(t,S) {
if (t == '(') t = ')';
else if (t == ')') t = '(';
}
FOR(d,1,N/2+1) solve(d);
ps(ans);
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?), set tle
* do smth instead of nothing and stay organized
*/
Compilation message
securitygate.cpp: In function 'void io::setIn(std::__cxx11::string)':
securitygate.cpp:112:35: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~
securitygate.cpp: In function 'void io::setOut(std::__cxx11::string)':
securitygate.cpp:113:36: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
768 KB |
Output is correct |
| 2 |
Correct |
4690 ms |
732 KB |
Output is correct |
| 3 |
Correct |
3 ms |
384 KB |
Output is correct |
| 4 |
Correct |
5 ms |
640 KB |
Output is correct |
| 5 |
Correct |
257 ms |
640 KB |
Output is correct |
| 6 |
Correct |
506 ms |
652 KB |
Output is correct |
| 7 |
Correct |
110 ms |
768 KB |
Output is correct |
| 8 |
Correct |
4780 ms |
636 KB |
Output is correct |
| 9 |
Correct |
4837 ms |
632 KB |
Output is correct |
| 10 |
Correct |
4546 ms |
640 KB |
Output is correct |
| 11 |
Correct |
99 ms |
768 KB |
Output is correct |
| 12 |
Correct |
2314 ms |
616 KB |
Output is correct |
| 13 |
Correct |
1531 ms |
632 KB |
Output is correct |
| 14 |
Correct |
753 ms |
632 KB |
Output is correct |
| 15 |
Execution timed out |
5067 ms |
548 KB |
Time limit exceeded |
| 16 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
768 KB |
Output is correct |
| 2 |
Correct |
4690 ms |
732 KB |
Output is correct |
| 3 |
Correct |
3 ms |
384 KB |
Output is correct |
| 4 |
Correct |
5 ms |
640 KB |
Output is correct |
| 5 |
Correct |
257 ms |
640 KB |
Output is correct |
| 6 |
Correct |
506 ms |
652 KB |
Output is correct |
| 7 |
Correct |
110 ms |
768 KB |
Output is correct |
| 8 |
Correct |
4780 ms |
636 KB |
Output is correct |
| 9 |
Correct |
4837 ms |
632 KB |
Output is correct |
| 10 |
Correct |
4546 ms |
640 KB |
Output is correct |
| 11 |
Correct |
99 ms |
768 KB |
Output is correct |
| 12 |
Correct |
2314 ms |
616 KB |
Output is correct |
| 13 |
Correct |
1531 ms |
632 KB |
Output is correct |
| 14 |
Correct |
753 ms |
632 KB |
Output is correct |
| 15 |
Execution timed out |
5067 ms |
548 KB |
Time limit exceeded |
| 16 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
768 KB |
Output is correct |
| 2 |
Correct |
4690 ms |
732 KB |
Output is correct |
| 3 |
Correct |
3 ms |
384 KB |
Output is correct |
| 4 |
Correct |
5 ms |
640 KB |
Output is correct |
| 5 |
Correct |
257 ms |
640 KB |
Output is correct |
| 6 |
Correct |
506 ms |
652 KB |
Output is correct |
| 7 |
Correct |
110 ms |
768 KB |
Output is correct |
| 8 |
Correct |
4780 ms |
636 KB |
Output is correct |
| 9 |
Correct |
4837 ms |
632 KB |
Output is correct |
| 10 |
Correct |
4546 ms |
640 KB |
Output is correct |
| 11 |
Correct |
99 ms |
768 KB |
Output is correct |
| 12 |
Correct |
2314 ms |
616 KB |
Output is correct |
| 13 |
Correct |
1531 ms |
632 KB |
Output is correct |
| 14 |
Correct |
753 ms |
632 KB |
Output is correct |
| 15 |
Execution timed out |
5067 ms |
548 KB |
Time limit exceeded |
| 16 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
768 KB |
Output is correct |
| 2 |
Correct |
4690 ms |
732 KB |
Output is correct |
| 3 |
Correct |
3 ms |
384 KB |
Output is correct |
| 4 |
Correct |
5 ms |
640 KB |
Output is correct |
| 5 |
Correct |
257 ms |
640 KB |
Output is correct |
| 6 |
Correct |
506 ms |
652 KB |
Output is correct |
| 7 |
Correct |
110 ms |
768 KB |
Output is correct |
| 8 |
Correct |
4780 ms |
636 KB |
Output is correct |
| 9 |
Correct |
4837 ms |
632 KB |
Output is correct |
| 10 |
Correct |
4546 ms |
640 KB |
Output is correct |
| 11 |
Correct |
99 ms |
768 KB |
Output is correct |
| 12 |
Correct |
2314 ms |
616 KB |
Output is correct |
| 13 |
Correct |
1531 ms |
632 KB |
Output is correct |
| 14 |
Correct |
753 ms |
632 KB |
Output is correct |
| 15 |
Execution timed out |
5067 ms |
548 KB |
Time limit exceeded |
| 16 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
768 KB |
Output is correct |
| 2 |
Correct |
4690 ms |
732 KB |
Output is correct |
| 3 |
Correct |
3 ms |
384 KB |
Output is correct |
| 4 |
Correct |
5 ms |
640 KB |
Output is correct |
| 5 |
Correct |
257 ms |
640 KB |
Output is correct |
| 6 |
Correct |
506 ms |
652 KB |
Output is correct |
| 7 |
Correct |
110 ms |
768 KB |
Output is correct |
| 8 |
Correct |
4780 ms |
636 KB |
Output is correct |
| 9 |
Correct |
4837 ms |
632 KB |
Output is correct |
| 10 |
Correct |
4546 ms |
640 KB |
Output is correct |
| 11 |
Correct |
99 ms |
768 KB |
Output is correct |
| 12 |
Correct |
2314 ms |
616 KB |
Output is correct |
| 13 |
Correct |
1531 ms |
632 KB |
Output is correct |
| 14 |
Correct |
753 ms |
632 KB |
Output is correct |
| 15 |
Execution timed out |
5067 ms |
548 KB |
Time limit exceeded |
| 16 |
Halted |
0 ms |
0 KB |
- |
