Permutation Graph, Minimum Cyclic shift

#include <bits/stdc++.h>
// #include <atcoder/all>
using namespace std;
#define int long long
#define all(x) (x).begin(), (x).end()
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pair<int, int>> vpi;
typedef pair<int, int> pi;
#define f first
#define s second
#define pb push_back
#define endl "\n"
#define yes cout << "YES" << endl
#define no cout << "NO" << endl
#define init(x, a) memset(x, a, sizeof(x))
const int mod1 = 1e9 + 7, mod2 = 998244353, INF = 2e18, N = 2e5 + 5, L = 19;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
// -----------------------------------------------------------------------------

void solve()
{
    int n;
    cin >> n;
    string s;
    cin >> s;
    vi p(n);
    for (int i = 0; i < n; i++)
    {
        cin >> p[i];
        p[i]--;
    }
    int ans = 1;
    // we have to find minimum k such that s= s[k:] + s[:k], minimum cyclic shift
    function<int(string &)> cycle = [&](string &s)
    {
        int n = s.size();
        for (int i = 1; i <= n; i++)
        {
            // s[i:] + s[:i], (i to end + 0 to i)
            if (s == s.substr(i) + s.substr(0, i))
            {
                return i;
            }
        }
        return n;
    };
    vi vis(n, 0);
    // permutaion cycle, all cycles are disjoint, and are shifted
    for (int i = 0; i < n; i++)
    {
        if (vis[i])
        {
            continue;
        }
        int x = i;
        string temp;
        while (!vis[x])
        {
            vis[x] = 1;
            temp += s[x];
            x = p[x];
        }
        // permuatation cycle got
        int shift = cycle(temp);
        ans /= gcd(ans, shift);
        ans *= shift;
    }
    cout << ans << endl;
    return;
}

signed main()
{
    // __START__;
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int t = 1;
    cin >> t;
    while (t--)
    {
        solve();
    }
    // __END__;
    return 0;
}