Adjacent Integers Converted to Float

Version: Phuoc Hung OJ Extended

Problem Statement

Given a nonnegative integer $n$, independently convert $n$ and $n+1$ to Python 3 float and determine whether the converted values are equal. Binary floating-point numbers have limited precision, so consecutive sufficiently large integers may map to the same value. Do not compare the original integers directly.

Input

The only line contains a nonnegative integer $n$.

Output

Print exactly True if float(n) equals float(n + 1), otherwise False.

Subtasks

• Subtask 1 (100 points): $0\le n\le2^{54}$.

Examples

Example 1

Input

9007199254740991

Output

False

Explanation. The converted values are 9007199254740991.0 and 9007199254740992.0 respectively. Comparing these two float values gives False.

Example 2

Input

9007199254740992

Output

True

Explanation. The converted values are 9007199254740992.0 and 9007199254740992.0 respectively. Comparing these two float values gives True.

Example 3

Input

9007199254740993

Output

False

Explanation. The converted values are 9007199254740992.0 and 9007199254740994.0 respectively. Comparing these two float values gives False.