A museum floor is tiled with a single row of n tiles (n is always even), and each tile carries a lowercase letter code identifying its color pattern. The original design was a perfect mirror image: reading the row from the left end should exactly match reading it from the right end, tile for tile. Over the years, some tiles were replaced with the wrong pattern. A restorer can re-lay any tile with any single lowercase letter of their choosing, one tile per operation. Given the current row of letters, determine whether the restorer can recover full mirror symmetry using at most two individual tile replacements in total.

Input format

• Line 1: an integer n, the number of tiles.
• Line 2: a string s of length n consisting of lowercase English letters — the current tile pattern, read left to right.

Output format

Print true if at most two tile replacements suffice to make s read the same forwards and backwards (a palindrome), and false otherwise.

Constraints

• 2 <= n <= 100000
• n is even.
• s consists only of lowercase English letters ('a'-'z') and has length exactly n.

6
abcxya

true

6
abcdef

false