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>
using namespace std;
const int SIZE=2000000;
bool is_prime[SIZE];
int main() {
    memset(is_prime,-1,sizeof(is_prime));
    for(int i=2;i*i<SIZE;i++) {
        if(!is_prime[i]) continue;
        for(int j=i*2;j<SIZE;j+=i) is_prime[j]=0;
    }
    vector<int> prime;
    for(int i=2;i<SIZE;i++) if(is_prime[i]) prime.push_back(i);
    int n;
    while(scanf("%d",&n),n) {
        int pos=lower_bound(prime.begin(),prime.end(),n)-prime.begin();
        if(prime[pos]==n) {printf("0\n");continue;}
        printf("%d\n",prime[pos]-prime[pos-1]);
    }
}