#include <bits/stdc++.h>
using namespace std;

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (a) - 1; i >= (b); i--)
#define SZ(a) (int)a.size()
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair
#define F first
#define S second

typedef long long LL;
typedef unsigned long long ULL;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef double db;

mt19937 rng(7447);

const int N = 256;
int mp[N];

void solve()
{
	int m;
	string s;
	cin >> m >> s;
	VI v(m);
	iota(ALL(v), 0);
	vector<ULL> pw(SZ(s));
	pw.back() = 1;
	RFOR (i, SZ(s) - 1, 0)
		pw[i] = pw[i + 1] * m;
		
	
	vector<int> alp;
	FOR (i, 0, SZ(s))
		alp.PB(s[i] - 'a');
	sort(ALL(alp));
	alp.resize(unique(ALL(alp)) - alp.begin());
	
	ULL g = 0;
	if (m > SZ(alp))
	{
		FOR (i, 0, SZ(alp))
		{
			ULL num = 0;
			FOR (j, 0, SZ(s))
			{
				if (s[j] - 'a' == alp[i])
					num += pw[j];
			}
			g = gcd(g, num);
		}
	}
	ULL x = 0;
	FOR (i, 0, SZ(s))
	{
		if (s[i] - 'a' == alp[0])
			x += pw[i];
	}
	FOR (i, 1, SZ(alp))
	{
		ULL y = 0;
		FOR (j, 0, SZ(s))
		{
			if (s[j] - 'a' == alp[i])
				y += pw[j];
		}
		if (y > x)
			y -= x;
		else
			y = x - y;
		g = gcd(g, y);
	}
	
	cout << g << '\n';
	
	
}

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(15);
	
	fill(mp, mp + N, -1);
	
	int t;
	cin >> t;
	while (t--)
	{
		solve();
	}
	
	return 0;
}