As any experienced programmer must know the famous problem of "Edit Distance", however this problem is considered an “alternating chain” if you have alternately made case sensitive.

Example: "AaAaAbB" "B" "a" "aBaCdEf"

Alternating chains are considered in our problem.

We only have one operation that is permitted in exchange for a lower or upper case Latin letter.

Given a string giving the minimum number of changes to be considered an alternating chain.

Input

A string with no spaces line containing only uppercase and lowercase letters, one for each line of maximum length 10^3 until end of file

Output

For each line print the minimum number of changes to the chain is a "chain alternately"

Example

Input:
AaAaB
ABaa
a
Output:
0
2
0