#include <iostream>
#include <cmath>
using namespace std;

int value[301];

int pow(int x, int n) {
  int ans = 1;
  for(int i = 0; i < n; i++) {
    ans *= x;
  }
  return ans;
}

bool isHeiho(int x) {
  return (double)((int)sqrt(x)) == sqrt(x);
}

void rec(int minI, int x, int maxX) {
  if(x == 0) {
    value[maxX]++;
    return;
  }
  for(int i = minI; i <= 17; i++) {
    int tmp = pow(i, 2);
    if(tmp <= x) rec(i, x-tmp, maxX);
    if(tmp > x) break;
  }
}

int main() {
  for(int i = 1; i <= 30; i++) {
    value[i] = 0;
  }

  while(1) {
    int price;
    cin >> price;
    if(price == 0) break;
    if(value[price] == 0) {
      rec(1, price, price);
    }
    cout << value[price] << endl;
  }
  return 0;
}
### Prompt

Please create a solution in cpp to the following problem:

People in Silverland use square coins. Not only they have square shapes but also their values are square numbers. Coins with values of all square numbers up to 289 (= 172), i.e., 1-credit coins, 4-credit coins, 9-credit coins, ..., and 289-credit coins, are available in Silverland.

There are four combinations of coins to pay ten credits:

* ten 1-credit coins,
* one 4-credit coin and six 1-credit coins,
* two 4-credit coins and two 1-credit coins, and
* one 9-credit coin and one 1-credit coin.



Your mission is to count the number of ways to pay a given amount using coins of Silverland.



Input

The input consists of lines each containing an integer meaning an amount to be paid, followed by a line containing a zero. You may assume that all the amounts are positive and less than 300.

Output

For each of the given amount, one line containing a single integer representing the number of combinations of coins should be output. No other characters should appear in the output.

Example

Input

2
10
30
0


Output

1
4
27

### Response

```cpp
#include <iostream>
#include <cmath>
using namespace std;

int value[301];

int pow(int x, int n) {
  int ans = 1;
  for(int i = 0; i < n; i++) {
    ans *= x;
  }
  return ans;
}

bool isHeiho(int x) {
  return (double)((int)sqrt(x)) == sqrt(x);
}

void rec(int minI, int x, int maxX) {
  if(x == 0) {
    value[maxX]++;
    return;
  }
  for(int i = minI; i <= 17; i++) {
    int tmp = pow(i, 2);
    if(tmp <= x) rec(i, x-tmp, maxX);
    if(tmp > x) break;
  }
}

int main() {
  for(int i = 1; i <= 30; i++) {
    value[i] = 0;
  }

  while(1) {
    int price;
    cin >> price;
    if(price == 0) break;
    if(value[price] == 0) {
      rec(1, price, price);
    }
    cout << value[price] << endl;
  }
  return 0;
}
```