Back Front

For the lowercase English letter α, let ord(α) denote the order of α in the alphabet, under the standard ordering a,b,c,…,z.

For example, ord(b)=2,ord(j)=10,0, and ord(z)=26.

You are given a string S containing N lowercase English letters.

You can perform the following 2 operations on it:

1. Choose a subsequence of the string that equals "back", and delete the subsequence from S.
2. Then, choose any character α such that ord(α) has at most two divisors, and insert α at the start of S.
3. Choose a subsequence of the string that equals "front", and delete the subsequence from S.
4. Then, choose any character α such that ord(α) has strictly more than two divisors, and append α to S.

You may perform these two operations as many times as you like (possibly, zero), and in any order.

Find the minimum possible length of the final string after doing so.