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<stdio.h>
#include<iostream>
using namespace std;
bool n[1299710]={};
int main(){
for(int i=3;i<1299710;i+=2){n[i]=true;
	for(int j=2;j*j<=i;j++)
		if(i%j==0){n[i]=false;break;}}
n[2]=true;
	int N;
while(1){
	cin>>N;if(N==0)break;
	int x=0;int y=0;int c=0;
	if(n[N]==true||N==1)c=0;
	else{
	for(int i=N;i<1299710;i++)
		if(n[i]==true){x=i;break;}
	for(int i=N;i>1;i--)
		if(n[i]==true){y=i;break;}
	c=x-y;
	
	}
	cout<<c<<endl;
}
return 0;
}