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
def sieve():
    L = 1299710
    primes = []
    isPrime = [ True for _ in range(L) ]
    for i in range(2, L):
        if isPrime[i]:
            primes.append(i)
            for j in range(i * i, L, i):
                isPrime[j] = False
    return primes

def getPrimeGap(num, primes):
    if num in primes:
        return 0

    for i in range(100000 - 1):
        if primes[i] < num and primes[i + 1] > num:
            return primes[i + 1] - primes[i]

if __name__ == '__main__':
    primes = sieve()
    while True:
        num = int(input())
        if num == 0:
            break

        print(getPrimeGap(num, primes))
