#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;

#define kane 17
const int m[kane] = {1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289};

int cnt =0;

int search(int num){
int maxx;
if(num == 0 || num == 1){
return 0;
}
for(maxx=0;num-m[maxx+1]>=0;maxx++);
return maxx;
}

void func(int num,int k){
//	cout<<num<<":"<<m[k]<<endl;
	if(num <= 3 || k==0){
		cnt++;
//		cout<<"☆"<<endl;
		return;
	}
	for(;k>=0;k--)
		func(num -m[k],min(k,search(num -m[k])));
}
int main(){
while(1){
int num;
cnt = 0;
cin>>num;
if(num == 0) break;
func(num,search(num));
cout << cnt << endl;
//cout<<search(num)<<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 <cstdio>
#include <algorithm>
using namespace std;

#define kane 17
const int m[kane] = {1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289};

int cnt =0;

int search(int num){
int maxx;
if(num == 0 || num == 1){
return 0;
}
for(maxx=0;num-m[maxx+1]>=0;maxx++);
return maxx;
}

void func(int num,int k){
//	cout<<num<<":"<<m[k]<<endl;
	if(num <= 3 || k==0){
		cnt++;
//		cout<<"☆"<<endl;
		return;
	}
	for(;k>=0;k--)
		func(num -m[k],min(k,search(num -m[k])));
}
int main(){
while(1){
int num;
cnt = 0;
cin>>num;
if(num == 0) break;
func(num,search(num));
cout << cnt << endl;
//cout<<search(num)<<endl;
}
return 0;
}
```