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Ex - Sequence of Substrings

Score : $600$ points

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.

7
0101010

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.

30
000011001110101001011110001001

9