Chef and Chefness

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Chef has a string S with length N. As Chef really likes his name, he defines the chefness of a string as the number of ways to find the string "chef" as a subsequence in S; formally, it's the number of ways to choose four indices i, j, k, l such that Si = 'c', Sj = 'h', Sk = 'e', Sl = 'f' and 1 ≤ i ≤ j ≤ k ≤ l ≤ N. For example, the chefness of "chehefc" is 3 (with subsequences given by indices (1,

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