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 <iostream>

using namespace std;

#define MAX 1500000
 
bool prime[MAX];
 
void make(){
    fill(prime,prime+MAX,true);
    prime[0] = prime[1] = false;
     
    for(int i = 2 ; i*i < MAX ; i++){
        if(prime[i]){
            for(int j = 2*i ; j < MAX ; j += i){
                prime[j] = false;
	    }
	}
    }
}
 
int main(){
    int n;
    make();
    while(cin >> n,n){
        int a,i;    
        if(prime[n]) cout << '0' << endl;
        else{
            for(i = n ; prime[i] != true ; i++);
            a = i;
            for(i = n ; prime[i] != true ; i--);
            cout << a-i << endl;
        }
    }
    return 0;
}