Problem:
Score : 1400 points

Problem Statement

Takahashi found an integer sequence (A_1,A_2,...,A_N) with N terms. Since it was too heavy to carry, he decided to compress it into a single integer.

The compression takes place in N-1 steps, each of which shorten the length of the sequence by 1. Let S be a string describing the steps, and the sequence on which the i-th step is performed be (a_1,a_2,...,a_K), then the i-th step will be as follows:

When the i-th character in S is M, let b_i = max(a_i,a_{i+1}) (1 ≦ i ≦ K-1), and replace the current sequence by (b_1,b_2,...,b_{K-1}).

When the i-th character in S is m, let b_i = min(a_i,a_{i+1}) (1 ≦ i ≦ K-1), and replace the current sequence by (b_1,b_2,...,b_{K-1}).

Takahashi decided the steps S, but he is too tired to carry out the compression. On behalf of him, find the single integer obtained from the compression.

Constraints

2 ≦ N ≦ 10^5

1 ≦ A_i ≦ N

S consists of N-1 characters.

Each character in S is either M or m.

Partial Scores

In the test set worth 400 points, there exists i (1 ≦ i < N-1) such that the first i characters in S are M, and the remaining characters are m, that is, S is in the form M...Mm...m.

In the test set worth 800 points, the odd-number-th characters in S are M, and the even-number-th characters are m, that is, S is in the form MmMmMm....

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N
S

Output

Print the single integer obtained from the compression.

Sample Input 1

4
1 2 3 4
MmM

Sample Output 1

3

The initial sequence ( 1 , 2 , 3 , 4 ) is compressed as follows:

After the first step, the sequence is ( 2 , 3 , 4 ).

After the second step, the sequence is ( 2 , 3 ).

After the third step, the sequence is ( 3 ).

Thus, the single integer obtained from the compression is 3.

Sample Input 2

5
3 4 2 2 1
MMmm

Sample Output 2

2

Sample Input 3

10
1 8 7 6 8 5 2 2 6 1
MmmmmMMMm

Sample Output 3

5

Sample Input 4

20
12 7 16 8 7 19 8 19 20 11 7 13 20 3 4 11 19 11 15 5
mMMmmmMMMMMMmMmmmMM

Sample Output 4

11

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import Control.Applicative

main :: IO ()
main = do
  getLine
  xs <- map read . words <$> getLine
  ops <- getLine
  let
    fu 'm' = min :: Integer -> Integer -> Integer
    fu 'M' = max
  print $ head $ foldl proc xs $ map fu ops

proc :: [a] -> (a -> a -> a) -> [a]
proc xs f = zipWith f xs $ tail xs