human
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.

What is a Python program to print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes)?
assistant
#Here is Python program to print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

T_ON = 0
DEBUG_ON = 0
MOD = 998244353

def solve():
    n = read_int()
    A = set()
    k = 1
    while True:
        a = k * (k+1) // 2
        if a >= n:
            break
        A.add(a)
        k += 1
    for a in A:
        if (n-a) in A:
            YES()
            return
    NO()

def solve2():
    A = read_ints()
    A.sort()
    a, b, c = A
    # (b-a) and (c-a) cannot be combined directly
    x = b - a + c - a
    q, r = divmod(x, 7)
    debug(a, b, c, x, q, r)
    a -= q
    if r:
        if (6-r) % 3 != 0:
            NO()
            return
        else:
            a -= (6-r) // 2 + 1
    if a >= 0 and a % 3 == 0:
        YES()
    else:
        NO()

def main():
    T = read_int() if T_ON else 1
    for i in range(T):
        solve()

def debug(*xargs):
    if DEBUG_ON:
        print(*xargs)

from collections import *

#---------------------------------FAST_IO---------------------------------------

import os
import sys
from io import BytesIO, IOBase
# region fastio

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if...