A composite number is a Smith number if its digit sum equals the sum of the digits of its prime factors, counted with multiplicity. Determine whether \(N\) is a Smith number.

Input

One line containing \(N\).

The input satisfies:

• \(1 \le N \le 10^18\)

Output

Print YES if \(N\) is a Smith number; otherwise, print NO.

Example

Input

1

Output

NO