Wide Flip

You are given a string S consisting of 0 and 1. Find the maximum integer K not greater than |S| such that we can turn all the characters of S into 0 by repeating the following operation some number of times.

• Choose a contiguous segment [l,r] in S whose length is at least K (that is, r-l+1\geq K must be satisfied). For each integer i such that l\leq i\leq r, do the following: if S_i is 0, replace it with 1; if S_i is 1, replace it with 0.

Constraints

• 1\leq |S|\leq 10^5
• S_i(1\leq i\leq N) is either 0 or 1.

Input

Input is given from Standard Input in the following format:

S

Output

Print the maximum integer K such that we can turn all the characters of S into 0 by repeating the operation some number of times.

Examples

Input

010

Output

2

Input

100000000

Output

8

Input

00001111

Output

4

inputFormat

Input

Input is given from Standard Input in the following format:

S

outputFormat

Output

Print the maximum integer K such that we can turn all the characters of S into 0 by repeating the operation some number of times.

Examples

Input

010

Output

2

Input

100000000

Output

8

Input

00001111

Output

4

样例

100000000

8