Valid lexicographical order

There are $n$ strings $s_1,s_2...s_n$ where each string contains characters from a strange alphabet system having an infinite number of distinct characters. You are given an array $arr_1,arr_2...arr_n$ containing $n$ positive integers such that $arr_i$ is the length of string $s_i$. Given that $s_1\leq s_2...\leq s_n$ holds lexicographically, find the minimum number of distinct characters that are