#include<iostream>
using namespace std;
long long dp[1001];
int main() {
	dp[0] = 1;
	for (int i = 1; i <= 31; i++) {
		for (int j = 0; j < 1000; j++) {
			if (i*i + j > 1000) { continue; }
			dp[i*i + j] += dp[j];
		}
	}
	int n;
	while (true) {
		cin >> n; if (n == 0) { break; }
		cout << dp[n] << 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>
using namespace std;
long long dp[1001];
int main() {
	dp[0] = 1;
	for (int i = 1; i <= 31; i++) {
		for (int j = 0; j < 1000; j++) {
			if (i*i + j > 1000) { continue; }
			dp[i*i + j] += dp[j];
		}
	}
	int n;
	while (true) {
		cin >> n; if (n == 0) { break; }
		cout << dp[n] << endl;
	}
	return 0;
}
```