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;
bool s[1300000];
int main(){
  for(int i=2;i*i<1299709;i++)
    if(!s[i])for(int j=2;j*i<1299709;j++)s[i*j]=1;
  int n;
  while(cin>>n&&n){
    int an=0;
    for(int i=n;s[i];i++)an++;
    for(int i=n;s[i];i--)an++;
    cout<<an<<endl;
  }
  return 0;
}