Separate the Numbers

A numeric string s is beautiful if it can be split into a sequence of two or more positive integers, a[1], a[2], ...a[n], satisfying the following conditions:

1. a[i] - a[i-1] = 1 for any 1 < i <= n (i.e. each element in the sequence is one more than the previous element).
2. No a[i] contains a leading zero. For example, we can split s = 10203 into the sequence {1, 02, 03}, but it is not beautiful because 02 and 03 have leading zeroes.
3. The contents of the sequence cannot be rearranged. For example, we can split s = 312 into the sequence {3, 1, 2}, but it is not beautiful because it breaks our first constraint (i.e. 1 - 3 ≠ 1).

Return either "YES x" where x is the smallest first number of the increasing sequence or "NO" if there is no valid sequence.

Examples

separate_numbers("1234") ➞ "YES 1"

separate_numbers("91011") ➞ "YES 9"

separate_numbers("99100") ➞ "YES 99"

separate_numbers("101103") ➞ "NO"

separate_numbers("010203") ➞ "NO"

Notes

N/A