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| #include <bits/stdc++.h>
#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")
#define MAX_N 22
#define INF 987654321
#define EPS 1e-9
#define ll long long
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vall3 vector<array<ll,3>>
#define all3 array<ll,3>
#define all5 array<ll,5>
#define vall5 vector<all5>
#define vll vector<ll>
#define vs vector<string>
#define usll unordered_set<ll>
#define vvs vector<vs>
#define vvll vector<vll>
#define all(a) begin(a), end(a)
using namespace std;
ll mod = 1e9 + 7;
ll fact[404];
ll dp[404][404][404];
ll gcd(ll p, ll q){
if(q==0) return p;
return gcd(q, p%q);
}
ll fac(ll n) {
if(fact[n]) return fact[n];
return fact[n] = (n * fac(n - 1)) % mod;
}
ll modpow(ll x, ll n) {
if(n == 0) return 1;
ll res = modpow(x, n>>1);
res = (res * res) % mod;
if(n&1) res = (res * x) % mod;
return res;
}
ll solve(ll n, string s) {
memset(dp, 0, sizeof dp);
for(ll i = 0; i <= n; i++)
for(ll j = 0; j <=n ; j++)
dp[i][j][1] = max(0ll, j - i + 1), dp[i][j][0] = 1;
ll p = (2 * fac(n)) % mod;
for(ll i = n - 1; i >= 0; i--) {
for(ll j = i + 1; j < n; j++) {
for(ll k = 2; k < n; k++) {
if(j - i + 1 < k) break;
if(s[i] == s[j]) {
dp[i][j][k] = (dp[i][j-1][k] + dp[i+1][j][k] - dp[i+1][j-1][k] + dp[i+1][j-1][k-2]) % mod;
p = (p + fac(k) * fac(n - k) % mod * dp[i+1][j-1][k-2]) % mod;
} else {
dp[i][j][k] = (dp[i][j-1][k] + dp[i+1][j][k] - dp[i+1][j-1][k] + mod) % mod;
}
}
}
}
return (p * modpow(fac(n), mod - 2)) % mod;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
ll tc;
cin >> tc;
fact[0] = fact[1] = 1;
for (ll i = 1; i <= tc; i++) {
ll n;
string s;
cin>>n>>s;
cout << "Case #" << i << ": "<<solve(n, s)<<endl;
}
return 0;
}
|
