【CF#192 A】Funky Numbers （二分，查找，二元组）

题干：

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, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

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.

题目大意：

给你一个数字N，问你是否存在两个数字A,B使得N=A(A+1)2+B(B+1)2N=A(A+1)2+B(B+1)2 

解题报告：

    优秀的二分，复杂度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 ;
}