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;

const int N = 1299800;

bool prime[N];

void makePrime(){
    for(int i = 2; i < N; i++) prime[i] = true;
    for(int i = 2; (i * i) < N; i++){
        if(!prime[i]) continue;
        for(int j = i + i; j < N; j += i){
            prime[j] = false;
        }
    }
}

int main(){
    makePrime();
    int n;
    while(cin >>n){
        if(n == 0) break;
        if(prime[n]){
            cout <<'0' <<endl;
            continue;
        }
        int top = n, tail = n;
        while(!prime[top]) top--;
        while(!prime[tail]) tail++;
        cout <<tail - top <<endl;
    }
    return 0;
}