Given a bit string S i.e containing "0" and "1" only. You can perform K number of operations (K>0) in an iterative way in the following manner:-

starting from K=1,
when K=1, remove one leftmost bit and append it to right.
when K=2, remove two leftmost bit one by one and append it to right one by one.
when K=3, remove three left most bit one by one and append it to right one by one.
when K=4, remove four left most bit one by one and append it to right one by one.
so on...

You have to print the minimum value of K (K > 0) so that we get our original input string S after K number of operations.

Input format :-

A sigle string S.

Output format :-

Print minimum value of K.

Constraints:-

2<=length of string<=10^5

Example:-

Input 1:-

1011

Output:-

7

Input 2:-

1101

Output:-

7

Input 3:-

11011

Output:-

4

Input 4:-

11010

Output:-

4

Input 5:-

01010

Output:-

4

Input 6:-

101010

Output:-

3

Input 7:-

111001

Output:-

3

Explanations:-

In 1st input S=1011, so starting from K=1,

K=1 , S=0111 (1011 -> 0111)
K=2 , S=1101 (0111 -> 1110 -> 1101)
K=3 , S=1110 (1101 -> 1011 -> 0111 -> 1110)
K=4 , S=1110 (1110 -> 1101 -> 1011 -> 0111 -> 1110)
K=5 , S=1101 (1110 -> 1101 -> 1011 -> 0111 -> 1110 -> 1101)
K=6 , S=0111 (1101 -> 1011 -> 0111 -> 1110 -> 1101 -> 1011 -> 0111)
K=7 , S=1011 (0111 -> 1110 -> 1101 -> 1011 -> 0111 -> 1110 -> 1101 -> 1011)

so answer is K=7.