Ridbit starts with an integer n.

In one move, he can perform one of the following operations: 

  * divide n by one of its proper divisors, or 
  * subtract 1 from n if n is greater than 1. 



A proper divisor is a divisor of a number, excluding itself. For example, 1, 2, 4, 5, and 10 are proper divisors of 20, but 20 itself is not.

What is the minimum number of moves Ridbit is required to make to reduce n to 1?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains a single integer n (1 ≤ n ≤ 10^9).

Output

For each test case, output the minimum number of moves required to reduce n to 1.

Example

Input


6
1
2
3
4
6
9


Output


0
1
2
2
2
3

Note

For the test cases in the example, n may be reduced to 1 using the following operations in sequence

1

2 \xrightarrow{} 1

3 \xrightarrow{} 2 \xrightarrow{} 1

4 \xrightarrow{} 2 \xrightarrow{} 1

6 \xrightarrow{} 2 \xrightarrow{} 1

9 \xrightarrow{} 3 \xrightarrow{} 2\xrightarrow{} 1
//Author: A_S_M_M@sud_P@rvez
#include<bits/stdc++.h>
using namespace std;
#define    MP ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define    For(i,n) for(int i=0;i<n;i++)
#define    forn(i,n) for(int i=1;i<=n;i++)
#define    fors(i,s) for(int i=0;i<s.size();i++)
#define    all(v) v.begin(),v.end()
#define    gcd(a, b) __gcd(a , b)
#define    lcm(a,b) (a*(b/__gcd(a,b)))
#define    Test  int T;cin>>T;for(int I=0;I<T;I++)
#define    min3(a,b,c)     min(a,min(b,c))
#define    max3(a,b,c)     max(a,max(b,c))
#define    min4(a,b,c,d)   min(min(a,b),min(c,d))
#define    max4(a,b,c,d)   max(max(a,b),max(c,d))
#define    Max(a)  *max_element(a,a+sizeof(a)/sizeof(a[0]))
#define    Min(a)  *min_element(a,a+sizeof(a)/sizeof(a[0]))
#define    nl     "\n"
#define    End    return 0 
#define    gt     greater<int>()
#define    ll     long long 
#define    mp     make_pair
#define    pb     push_back
#define    vi     vector<int>
#define    vl     vector<ll>
#define    mod    1000000007
#define    sp(n)  fixed<<setprecision(n)
#define    pi     acos(-1)

int main()
{
MP;
    Test 
    {
        int n;
        cin>>n;
        if(n>3)
        {
            if(n%2)cout<<3<<nl;
            else cout<<2<<nl;
        }
        else if(n==0)cout<<0<<nl;
        else cout<<n-1<<nl;
    }
    cerr<<endl<<(float)clock()/(float)CLOCKS_PER_SEC<<" sec"<<endl;
End;
}
