Vault Code Factorial Consistency

A vault manufacturer engraves every lock with an n-digit combination code (the code never begins with a leading zero unless it is the single-digit code 0). Security auditors compute the code's ignition value: the sum, over every digit d appearing in the code, of d! (with 0! = 1). A code is declared self-consistent if some rearrangement of its own digits, written without any extra leading zeros, reproduces the ignition value exactly -- equivalently, the decimal representation of the ignition value must use exactly the same digits, the same number of times, as the code itself. Determine whether the given code is self-consistent.

Input format

A single line containing the code, a string of decimal digits, 1 <= length <= 18, with no leading zero unless the code is exactly 0.

Output format

Print true if the code is self-consistent, otherwise print false.

Constraints

• 1 <= |code| <= 18
• code consists only of the characters '0'-'9'
• code has no leading zero unless code is exactly "0"

145

true

230

false