Power Quintet

By Kay Akashi

Time: 1000 ms

Memory: 256000 kB

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Problem Statement

Given an integer $N$ , judge if there's any combination of $5$ non-negative integers $(a, b, c, d, e)$ such that $a^{a} + b^{b} + c^{c} + d^{d} + e^{e} = N$ .

Constraints

$0 \leq N \leq 10^{5}$ .

Input

The input consists of a single integer, $N$ .

Output

If there's any combination that satisfies the outlined condition, output "Yes". Otherwise, "No" (case-specific).

Examples

Input

Output

Yes

Explanation

$(a, b, c, d, e) = (3, 1, 4, 1, 5)$ satisfies the condition.

Input

Output

No

Explanation

Be noted that if $(a, b, c, d, e) = (0, 0, 0, 0, 0)$ the resulting value is $5$ .

Power Quintet

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Problem Statement

Constraints

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Output

Examples

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Explanation

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Explanation