N cells are arranged in a row. Some of them may contain tokens. You are given a string s that consists of 0s and 1s. If the i-th character of s is 1, the i-th cell (from left) contains a token. Otherwise, it doesn't contain a token.

Snuke wants to perform the following operation as many times as possible. In each operation, he chooses three consecutive cells. Let's call the cells X, Y, Z from left to right. In order for the operation to be valid, both X and Z must contain tokens and Y must not contain a token. Then, he removes these two tokens and puts a new token on Y.

How many operations can he perform if he performs operations in the optimal way?

Constraints

• $1 \leq N \leq 500,000$
• |s| = N
• Each character in s is either 0 or 1.

Input

Input is given from Standard Input in the following format:

N
s

Output

Print the answer.

Examples

Input

7
1010101

Output

2

Input

50
10101000010011011110001001111110000101010111100110

Output

10

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