題幹：

As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as , where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256

Output

YES

Input

512

Output

NO

Note

In the first sample number .

In the second sample number 512 can not be represented as a sum of two triangular numbers.

解題報告：

    優秀的二分，複雜度sqrtnlogn

#include<bits/stdc++.h>

using namespace std;

int main()
{
	int n;
	cin>>n;
	int tmp,key;
	int l ,r,mid;
	n*=2;
	for(int i = 1; i<=sqrt(n); i++) {
		tmp = i * (i+1);
		key = n-tmp;
		l = i;
		r = sqrt(n);
		while(l<=r) {
			mid = (l+r)/2;
			if(mid * (mid+1) < key) l=mid+1;
			else if(mid*(mid+1)>key) r = mid-1;
			else {
				printf("YES\n");return 0 ;
			}
		}
	}
	printf("NO\n");
	return 0 ;
}