N. Count Permutationstime limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a string s with length n-1 whose characters are either \texttt{<} or \texttt{>}.Count the permutations p_1, \, p_2, \, \dots, \, p_n of 1, \, 2, \, \dots, \, n such that, for all i = 1, \, 2, \, \dots, \, n - 1, if s_i is \texttt{<} then p_i < p_{i+1} and if s_i is \texttt{>} then p_i > p_{i+1}.Since this number can be very large, compute its logarithm in base 2.InputThe first line contains a single integer n (2 \le n \le 100\,000).The second line contains a string s of length n-1; each character of s is either \texttt{<} or \texttt{>}.OutputPrint the logarithm in base 2 of the number of permutations satisfying the constraints described in the statement.Your answer is considered correct if its absolute or relative error does not exceed 10^{-6}. Formally, let your answer be x and let the correct answer be y. Your answer is accepted if and only if \frac{|x - y|}{\max{(1, |y|)}} \le 10^{-6}.ExamplesInput
2
<
Output
0.0000000000
Input
3
<>
Output
1.0000000000
Input
5
><<<
Output
2.0000000000
Input
10
<><<<<<>>
Output
9.8281364842
NoteIn the first sample, there is only one valid permutation, that is [2, 1]. Since \log_2(1)=0, the correct output is 0.In the second sample, there are 2 valid permutations, that are [3, 1, 2] and [2, 1, 3]. Since \log_2(2)=1, the correct output is 1.In the third sample, there are 4 valid permutations, that are [1, 5, 4, 3, 2], [2, 5, 4, 3, 1], [3, 5, 4, 2, 1], [4, 5, 3, 2, 1]. Since \log_2(4)=2, the correct output is 2.In the fourth sample, there are 909 valid permutations. Notice that \log_2(909)=9.828136484194\ldots
2
<

0.0000000000 
['math', '*3500']