Squadron Beacon Convergence Cost

A squadron of n drones flies in a single line, numbered 0 through n-1 from the front of the formation to the back. Each drone's identification beacon currently glows one of two colors, encoded as a binary string s of length n, where s[i] is '0' if the beacon at position i glows amber and '1' if it glows cyan.

The squadron leader can issue a resync command that targets a contiguous block of k drones counted from the very front of the line (for any 1 <= k <= n), or a contiguous block of k drones counted from the very back of the line. Issuing either command instantly toggles the color of every beacon inside the chosen block (amber becomes cyan and cyan becomes amber), and costs exactly k energy units -- one unit per drone touched.

The leader wants every beacon in the line to end up glowing the same color, using any number of resync commands in any order, while spending as little total energy as possible.

Input format

• Line 1: an integer n.
• Line 2: a string s of length n consisting only of the characters '0' and '1'.

Output format

Print a single integer: the minimum total energy needed to make every beacon glow the same color.

Constraints

• 1 <= n <= 100000
• s has length exactly n and consists only of '0' and '1'.

4
0011

2

2
10

1