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>
#include<cstdio>
#include<cstring>
using namespace std;
bool sosu[1299710];
void SOSU(){
  memset(sosu,false,sizeof(sosu));
  for(int i=2;i<1299710;i++){
    if(sosu[i]==false){
      for(int j=2;i*j<1299710;j++){
	sosu[i*j]=true;
      }
    }
  }
}
int main(){
  int n,sum,lI,lII;
  SOSU();
  while(1){
    sum=0;
    cin >> n;
    if(n == 0) break;
    for(lI=n;sosu[lI]==true && lI>=2;lI--);
    for(lII=n;sosu[lII]==true;lII++);
    cout << lII-lI << endl;
  }
}