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;
int isPrime(int n){
  for(int i=2;i*i<=n;i++) if(n%i==0) return 0;
  return 1;
}
int main(){
  int i,j,dp[1500000]={},c;
  i=2;
  
  while(i<1500000){
    c=1;
    dp[i]=0;
    while(isPrime(i+c)==0){
      c++;
    }
    if(i+c<1500000){
      for(j=i+1;j<i+c;j++) dp[j]=c;
      dp[i+c]=0;
    }
    i+=c;
  }
  int n;
  cin >> n;
  while(n!=0){
    cout << dp[n] << endl;
    cin >> n;
  }
  return 0;
}