Problem Statement

You are given a string $S = s_1 s_2 \ldots s_N$ of length $N$ consisting of $0$'s and $1$'s.

Find the maximum integer $K$ such that there is a sequence of $K$ pairs of integers $\big((L_1, R_1), (L_2, R_2), \ldots, (L_K, R_K)\big)$ that satisfy all three conditions below.

• $1 \leq L_i \leq R_i \leq N$ for each $i = 1, 2, \ldots, K$.
• $R_i \lt L_{i+1}$ for $i = 1, 2, \ldots, K-1$.
• The string $s_{L_i}s_{L_i+1} \ldots s_{R_i}$ is strictly lexicographically smaller than the string $s_{L_{i+1}}s_{L_{i+1}+1}\ldots s_{R_{i+1}}$.

Constraints

• $1 \leq N \leq 2.5 \times 10^4$
• $N$ is an integer.
• $S$ is a string of length $N$ consisting of $0$'s and $1$'s.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the answer.