The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24, 25, 26, 27, 28) between 23 and 29 is a prime gap of length 6.

Your mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap contains k.



Input

The input is a sequence of lines each of which contains a single positive integer. Each positive integer is greater than 1 and less than or equal to the 100000th prime number, which is 1299709. The end of the input is indicated by a line containing a single zero.

Output

The output should be composed of lines each of which contains a single non-negative integer. It is the length of the prime gap that contains the corresponding positive integer in the input if it is a composite number, or 0 otherwise. No other characters should occur in the output.

Example

Input

10
11
27
2
492170
0


Output

4
0
6
0
114
#include <bits/stdc++.h>
#define Msize 1300000
using namespace std;
 
bool prime[Msize] = {0};
 
void setp(){
    prime[0] = prime[1] = 1;
    for(int i = 2;i < Msize;++i)
        if(!prime[i])
            for(int j = 2;j * i < Msize;++j)
                prime[i * j] = 1;
}
 
int x;
 
int solve();
 
int main(){
    setp();
    while(1){
        cin >> x;
        if(x == 0)break;
        cout << solve() << endl;
    }
    return 0;
}
 
int solve(){
    if(!prime[x])return 0;
    int ans = 0,now = x;
    while(prime[now])++ans,++now;
    now = x;
    while(prime[now])++ans,--now;
    return ans;
}

