Problem: "We've tried solitary confinement, waterboarding and listening to Just In Beaver, to no avail. We need something extreme."
"Little Alena got an array as a birthday present..."
The array b of length n is obtained from the array a of length n and two integers l and r (l ≤ r) using the following procedure:
b1 = b2 = b3 = b4 = 0.
For all 5 ≤ i ≤ n:
- bi = 0 if ai, ai - 1, ai - 2, ai - 3, ai - 4 > r and bi - 1 = bi - 2 = bi - 3 = bi - 4 = 1
- bi = 1 if ai, ai - 1, ai - 2, ai - 3, ai - 4 < l and bi - 1 = bi - 2 = bi - 3 = bi - 4 = 0
- bi = bi - 1 otherwise
You are given arrays a and b' of the same length. Find two integers l and r (l ≤ r), such that applying the algorithm described above will yield an array b equal to b'.
It's guaranteed that the answer exists.
Input Format: The first line of input contains a single integer n (5 ≤ n ≤ 105) — the length of a and b'.
The second line of input contains n space separated integers a1, ..., an ( - 109 ≤ ai ≤ 109) — the elements of a.
The third line of input contains a string of n characters, consisting of 0 and 1 — the elements of b'. Note that they are not separated by spaces.
Output Format: Output two integers l and r ( - 109 ≤ l ≤ r ≤ 109), conforming to the requirements described above.
If there are multiple solutions, output any of them.
It's guaranteed that the answer exists.
Note: In the first test case any pair of l and r pair is valid, if 6 ≤ l ≤ r ≤ 109, in that case b5 = 1, because a1, ..., a5 < l.