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 is given from Standard Input in the following format:

```
$N$
$S$
```

Print the answer.

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

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≥4, there is no sequence $((L_1,R_1),(L_2,R_2),…,(L_K,R_K))$ satisfying the condition.