Recently, Timofey started studying algorithms and is currently learning about sorting. To reinforce the material, Timofey decided to practice on a string S of length N, consisting of zeros and ones. Sorting the entire string would be too simple, so Timofey decided to sort substrings of S, meaning he can perform the following operation:

To train well, Timofey set himself a goal. He wants to be able to transform the string S into a palindrome by applying the substring sorting operation an unlimited number of times (possibly zero). Can Timofey achieve his goal?

A palindrome is a string that reads the same forwards and backwards.

The first line contains a single integer N — the length of the string S (1 ≤ N ≤ 10⁵).

The second line contains the string S, consisting only of the characters 0 and 1.

Print “YES” if there exists a sequence of operations that transforms the string S into a palindrome, and “NO” otherwise.

In the first example, the string 010011110010 can be obtained:

• First, sort l = 4, r = 6, resulting in 010011110100.
• Then, sort l = 10, r = 11, resulting in 010011110010.