It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For example, 10 can be represented by the sum of two prime numbers, 7 + 3 and 5 + 5.

Write a program that inputs the integer n and outputs how many combinations of n are the sum of two prime numbers. However, n must be 4 or more and 50,000 or less. Also, the n entered is not always even.



Input

Given multiple datasets. Each dataset is given n on one row. When n is 0, it is the last input. The number of datasets does not exceed 10,000.

Output

For each dataset, output the number of combinations in which n is the sum of two prime numbers on one line.

Example

Input

10
11
0


Output

2
0
#include <stdio.h>
#define max 50010

int main(void) {
  long long i, j, k, n;
  bool prime[max];
  for(i = 0; i < max; ++i) prime[i] = true;
  prime[0] = prime[1] = false;
  for(i = 2; i < 250; ++i) if(prime[i]) for(j = 2; i * j < max; ++j) prime[i * j] = false;
  while( 1 ) {
    int ans = 0;
    scanf("%lld", &n);
    if(!n) break;
    for(i = 2; i <= n / 2; ++i) if(prime[i] && prime[n - i]) ++ans;
    printf("%d\n", ans);
  }
  return 0;
} 
