DMOPC '18 Contest 3 P3 - Bob and Math Class

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Points: 10 (partial)
Time limit: 2.0s
Memory limit: 256M

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Problem type

Bob has a pop quiz in math! Fortunately, it's only a true and false quiz. He has already finished and is checking over his answers to the N questions. His answers are a string of N Ts and Fs. Bob calls an array suspicious if it contains a subarray of only Ts or only Fs such that the length of the subarray is at least half of the length of the entire array. For example, TTTTFTF is a suspicious subarray since it contains TTTT while TFTTTFT is not suspicious. Given Bob's answers, how many of its subarrays are suspicious?

Constraints

Subtask 1 [10%]

1\le N\le 400

Subtask 2 [30%]

1\le N\le 2\ 000

Subtask 3 [40%]

1\le N\le 200\ 000

Subtask 4 [20%]

1\le N\le 1\ 000\ 000

Input Specification

The first line contains a single integer, N.
The next line contains a string of N characters, either T or F.

Output Specification

Output a single integer, the number of suspicious subarrays.

Sample Input 1

5
TFTFF

Sample Output 1

11

Explanation of Sample 1

The 11 suspicious subarrays are

T
 F
  T
   F
    F
TF
 FT
  TF
   FF
  TFF
 FTFF

Sample Input 2

5
TFTFT

Sample Output 2

9

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