#include <iostream>
#include <iomanip>
#include <vector>
#include <array>
#include <string>
#include <stack>
#include <queue>
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <set>
#include <tuple>
#include <cmath>
#include <algorithm>
#include <functional>
#include <numeric>
#include <cfloat>
#include <climits>
#include <cassert>
#include <random>
#include <fstream>

int main() {
	std::vector<int> pattern(300, 0); pattern[0] = 1;
	for (auto i = 1; i <= 17; ++i) {
		const auto price = i * i;
		for (auto j = 0; j + price < pattern.size(); ++j) {
			pattern[j + price] += pattern[j];
		}
	}
	while (true) {
		int n; std::cin >> n; if (n == 0) break;
		std::cout << pattern[n] << '\n';
	}
}


### Prompt

Your task is to create a CPP solution 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 <iomanip>
#include <vector>
#include <array>
#include <string>
#include <stack>
#include <queue>
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <set>
#include <tuple>
#include <cmath>
#include <algorithm>
#include <functional>
#include <numeric>
#include <cfloat>
#include <climits>
#include <cassert>
#include <random>
#include <fstream>

int main() {
	std::vector<int> pattern(300, 0); pattern[0] = 1;
	for (auto i = 1; i <= 17; ++i) {
		const auto price = i * i;
		for (auto j = 0; j + price < pattern.size(); ++j) {
			pattern[j + price] += pattern[j];
		}
	}
	while (true) {
		int n; std::cin >> n; if (n == 0) break;
		std::cout << pattern[n] << '\n';
	}
}


```