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

int n,m;
string a;
ll k[26];
int num[26];
void solve(){
    memset(k,0,sizeof(k));
    memset(num,-1,sizeof(num));
    cin>>m>>a;
    if(m==2){
        ll ans=1;
        for(int i=1;i<n;++i){
            ans*=2;
            if(a[i]==a[0])++ans;
        }
        cout<<ans<<'\n';
        return;
    }
    n=a.length();
    ll pw=1;
    for(int i=n-1;i>=0;--i)
        k[a[i]-'a']+=pw,pw*=m;
    int cnt=0;
    num[a[0]-'a']=1;
    for(int i=1;i<n;++i){
        if(num[a[i]-'a']==-1){
            num[a[i]-'a']=cnt;
            if(cnt==0)cnt+=2;
            else ++cnt;
        }
    }
    ll ans=0;
    for(int i=0;i<26;++i)if(num[i]!=-1)
        ans+=num[i]*k[i];
    for(int i=0;i<26;++i)if(num[i]!=-1)
        ans=__gcd(ans,abs(k[i]-k[a[0]-'a']));
    if(cnt<m){
        for(int i=0;i<26;++i)if(num[i]!=-1)
            ans=__gcd(ans,k[i]);
    }
    cout<<ans<<'\n';
}

int main(){
    ios::sync_with_stdio(0);cin.tie(0);
    int T;
    cin>>T;
    while(T--)solve();
}