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 <vector>
#include <string.h>

using namespace std;
bool IsPrime[1300000];
vector<int> Prime;

void calc()
{
	memset(IsPrime, 1, sizeof(bool) * 1300000);
	for(int i = 2; i < 1300000; ++i)
	{
		if(IsPrime[i])
		{
			Prime.push_back(i);
			for(int j = 2 * i; j < 1300000; j += i)
			{
				IsPrime[j] = false;
			}
		}
	}
}

void solve()
{
	calc();
	int n;
	while(cin >> n, n)
	{
		if(IsPrime[n])
		{
			cout << 0 << endl;
		}
		else
		{
			int pos = 0;
			while(Prime[pos] < n)
			{
				pos++;
			}
			cout << Prime[pos] - Prime[pos - 1] << endl;
		}
	}
}

int main()
{
	solve();
	return(0);
}