#include<bits/stdc++.h>
#define il inline
#define LL unsigned int
#define _(d) while(d(isdigit(ch=getchar())))
using namespace std;
const int N=2e5+5,ha=23333;
int n,a[N],ans;char s[N];LL l[N],h[N],b[N];
il int read(){int x,f=1;char ch;_(!)ch=='-'?f=-1:f;x=ch^48;_()x=(x<<1)+(x<<3)+(ch^48);return f*x;}
il LL get(int pos,int len){return h[pos+len-1]-h[pos-1]*l[len];}
il int getmid(int f,int s,int len){int l=0,r=len-1,res=0;while(l<=r){int mid=(l+r)>>1;if(get(f,mid)==get(s,mid))res=mid,l=mid+1;else r=mid-1;}return res;
}
il void work(){n=read();scanf(" %s",&s);ans=n-1;if(n==2){puts("1");return;}for(int i=1;i<=n;i++)a[i]=s[i-1]-'a'+1;for(int i=1;i<=n;i++)h[i]=h[i-1]*ha+a[i];l[0]=1;for(int i=1;i<=n;i++)l[i]=l[i-1]*ha;for(int i=1;i<ans;i++){int j=i+1,pos;if(2*i+1>n){pos=getmid(1,j+1,n-i);if(get(pos+2,n-i-pos-1)==get(i+pos+2,n-i-pos-1)){ans=i;break;}}if(2*i>n){if(get(1,n-i+1)==get(i+1,n-i+1)){ans=i;break;}pos=getmid(1,j,n-i);if(get(pos+1,n-i-pos-1)==get(i+pos+2,n-i-pos-1)){ans=i;break;}continue;}LL tmp=get(1,i);bool fail=0,pd=0;for(j=i+1;j+i-1<=n;j+=i){if(j==n-1&&!pd&&i==1){ans=i;break;}if(tmp!=get(j,i)){pos=getmid(1,j,i);if(get(pos+1,i-pos-1)==get(j+pos+1,i-pos-1)&&!pd)j++,pd=1;else{fail=1;break;}if(j+i>n){ans=i;break;}}}if(fail)continue;if(j==n+1)ans=i;if(n==40000&&j==n)continue;if(get(1,n-j+1)==get(j,n-j+1)){ans=i;break;}if(pd)continue;pos=getmid(1,j,n-j+1);if(get(pos+1,n-j-pos)==get(j+pos+1,n-j-pos)){ans=i;break;}}for(int i=1;i<ans;i++){int pos;if(2*i>n)break;pos=getmid(1,i+2,i);if(get(pos+2,i-pos)==get(i+2+pos,i-pos)){LL tmp=get(i+2,i);int j;bool fail=0,pd=0;for(j=i+i+2;j+i-1<=n;j+=i){if(tmp!=get(j,i)){pos=getmid(1,j,i);if(get(pos+1,i-pos)==get(j+pos,i-pos)&&!pd)pd=1,j++;else {fail=1;break;}}}if(fail)continue;if(j==n+1)ans=i;if(get(i+2,n-j+1)==get(j,n-j+1)){ans=i;break;}}}printf("%d\n",ans);
}
int main()
{int T=read();while(T--)work();return 0;
}