As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as $\text{[math]}$ , 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).

Note

In the first sample number $\text{[math]}$ .

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

Funky Numbers

Examples