Leetcode 3343. Count Number of Balanced Permutations

Count the distinct permutations of a digit string (length ≤ 80, digits 0–9 with repeats) whose sum of digits at even indices equals the sum at odd indices. Because of duplicates and large n, this requires a combinatorial/DP approach that assigns digit counts to even/odd positions and returns the count modulo 1e9+7.