Funky Numbers

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.

inputFormat

Input

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

outputFormat

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.

样例

512

NO

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