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 <math.h>
#define MAXNUM 1299709

int main(void){
	int flag[MAXNUM + 1], i, j, n;
	for(i = 0;i <= MAXNUM;i++)
		flag[i] = 1;
	for(i = 2;i <= sqrt((double)MAXNUM);i++){
		for(j = i * 2;j <= MAXNUM;j += i)
			flag[j] = 0;
	}
	flag[0] = flag[1] = 0;
	while(1){
		scanf("%d",&n);
		if(!n)
			break;
		for(i = n;!flag[i];i++);
		for(j = n;!flag[j];j--);
		printf("%d\n",i - j);
	}
	return 0;
}