Autobiographical Numbers

An autobiographical number is a number where the i-th digit (starting from 0) describes the number of times digit i appears in the number. Formally, if a number is represented as \(d_0d_1\dots d_{n-1}\), then for every \(i\) in \(\{0,1,\dots,n-1\}\), the following must hold:

[ d_i = \text{number of occurrences of } i \text{ in the number}, ]

For example, 1210 is an autobiographical number because it has 1 zero, 2 ones, 1 two, and 0 threes. Your task is to determine if a given number is an autobiographical number.

inputFormat

The input consists of a single integer \(N\) given via standard input (stdin).

outputFormat

Output a single line to standard output (stdout) containing True if the number is an autobiographical number, or False otherwise.

1210

True