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 $s_{L_{i+1}}s_{L_{i+1}+1}\ldots s_{R_{i+1}}$.

Input

Input is given from Standard Input in the following format:
N
S

Output

Print the answer.

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.

Sample Input 1

7
0101010

Sample Output 1

3

For K = 3, one sequence satisfying the conditition is (L_1, R_1) = (1, 1), (L_2, R_2) = (3, 5), (L_3, R_3) = (6, 7).
Indeed, s_1 = 0 is strictly lexicographically smaller than s_3s_4s_5 = 010, and s_3s_4s_5 = 010 is strictly lexicographically smaller than s_6s_7 = 10.
For $K \geq 4,$ there is no sequence $\big((L_1, R_1), (L_2, R_2), \ldots, (L_K, R_K)\big)$ satisfying the condition.

Sample Input 2

30
000011001110101001011110001001

Sample Output 2

9

见题面 Input 部分

见题面 Output 部分