Some positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive integer have? For example, the integer 53 has two representations 5 + 7 + 11 + 13 + 17 and 53. The integer 41 has three representations 2 + 3 + 5 + 7 + 11 + 13, 11 + 13 + 17, and 41. The integer 3 has only one representation, which is 3. The integer 20 has no such representations. Note that summands must be consecutive prime numbers, so neither 7 + 13 nor 3 + 5 + 5 + 7 is a valid representation for the integer 20.

Your mission is to write a program that reports the number of representations for the given positive integer.



Input

The input is a sequence of positive integers each in a separate line. The integers are between 2 and 10 000, inclusive. The end of the input is indicated by a zero.

Output

The output should be composed of lines each corresponding to an input line except the last zero. An output line includes the number of representations for the input integer as the sum of one or more consecutive prime numbers. No other characters should be inserted in the output.

Example

Input

2
3
17
41
20
666
12
53
0


Output

1
1
2
3
0
0
1
2
//Shunji Lin 08-144505

#include <iostream>
#include <queue>
#include <cstdlib>
#include <vector>

using namespace std;


int main() {
  // create a vector to store inputs
  vector<int> inputs;
  int n_inputs = 0; // number of inputs
  int max_prime = 0; // max prime (to generate vector of prime numbers)
  int input;
  while (cin >> input) { // read input
    if (input == 0) break;
    if (input > max_prime) max_prime = input;
    ++n_inputs;
    inputs.push_back(input);
  }

  //create bool of prime numbers (index)
  vector<bool> primes_bool(max_prime + 1, true); 


  //Sieve of Eratosthenes (algorithm for generating prime numbers)
  //https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
  
  int cur_prime = 2; // first prime
  
  while (cur_prime <= max_prime) {
    if (primes_bool[cur_prime] == true) { // if prime
      for (int l = cur_prime * 2; l <= max_prime; l += cur_prime) { 
	primes_bool[l] = false; // set all greater multiples to false (not prime)
      }
    }
    ++cur_prime;
  }

  //solve for each inputs
  for (int i = 0; i < n_inputs; ++i) {
    queue<int> primes_Q; // queue of primes up to value of input
    int cur_input = inputs[i];
    for (int j = 2; j <= cur_input; ++j) {
      if (primes_bool[j] == true) { //if prime
	primes_Q.push(j);
      }
    }
    
    queue<int> sum_Q; //queue to track sum of consequetive primes

    int count = 0; //count of sums
    int cur_sum = 0; //dynamic sum

    while (true) {
      if (cur_sum == cur_input) {
	++count;
	cur_sum -= sum_Q.front();
	sum_Q.pop();
      } else if (cur_sum < cur_input) {
	if (primes_Q.empty()) break; // terminate
	cur_sum += primes_Q.front();
	sum_Q.push(primes_Q.front());
	primes_Q.pop();
      } else if (cur_sum > cur_input) {
	cur_sum -= sum_Q.front();
	sum_Q.pop();
      }
    }
    cout << count << endl;
  }
}
    