We say that a binary string (a string containing only characters '0' and '1') is pure if it does not contain either of the strings "0101" or "1010" as a subsequence.
Recall that string T is a subsequence of string S if we can delete some of the letters of S (possibly none) such that the resulting string will become T.
You are given a binary string $S$ with length $N$. We want to make this string pure by deleting some (possibly zero) characters from it. What is the minimum number of characters we have to delete?

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single string $S$ with length $N$.

-----Output-----
For each test case, print a single line containing one integer — the minimum number of characters we have to delete from $S$.

-----Constraints-----
- $1 \le T \le 40$
- $1 \le N \le 1,000$
- $S$ contains only characters '0' and '1'

-----Example Input-----
4
010111101
1011100001011101
0110
111111

-----Example Output-----
2
3
0
0

-----Explanation-----
Example case 1: We can delete the first and third character of our string. There is no way to make the string pure by deleting only one character.
Example case 3: The given string is already pure, so the answer is zero.

Difficulty: interview

Starter code:

Solutions:
# cook your dish here
import math;
from math import gcd,sqrt,floor,factorial,ceil
from bisect import bisect_left,bisect_right
import bisect;
import sys;
from sys import stdin,stdout
import os
sys.setrecursionlimit(pow(10,7))
import collections
from collections import defaultdict,Counter
from statistics import median
# input=stdin.readline
# print=stdout.write
from queue import Queue
inf = float("inf")
from operator import neg;
mod=pow(10,9)+7
def fun(l):
 m=[[l[0]]]
 for i in range(1,n):
  if m[-1][-1]==l[i]:
   m[-1]+=[l[i]]
  else:
   m.append([l[i]])
 count=[]
 for i in range(len(m)):
  count.append(len(m[i]))
 return count;
def function(l1,index,prev,count):
 tuple=(index,prev,count)
 if tuple in dict:
  return dict[tuple]
 n=len(l1)
 if index==n:
  return 0;
 if count>=3:
  if index%2==prev:
   dict[tuple]=function(l1,index+1,prev,count)
   return function(l1,index+1,prev,count)
  else:
   dict[tuple]=l1[index]+function(l1,index+1,prev,count);
   return dict[tuple]
 if prev==None:
  skip=l1[index]+function(l1,index+1,prev,count)
  not_skip=function(l1,index+1,index%2,count+1)
  maxa=min(skip,not_skip)
  dict[tuple]=maxa
  return maxa;

 if index%2==prev:
  dict[tuple]=function(l1,index+1,index%2,count)
  return dict[tuple]
 if index%2!=prev:
  skip=l1[index]+function(l1,index+1,prev,count)
  not_skip=function(l1,index+1,index%2,1+count)
  maxa = min(skip, not_skip)
  dict[tuple]=maxa
  return maxa;

t=int(input())
for i in range(t):
 s=input()
 l=list(s)
 n=len(l)
 l=[int(i) for i in l]
 l1=fun(l)
 dict=defaultdict(int)
 theta=function(l1,0,None,0)
 print(theta)


# cook your dish here
import math;
from math import gcd,sqrt,floor,factorial,ceil
from bisect import bisect_left,bisect_right
import bisect;
import sys;
from sys import stdin,stdout
import os
sys.setrecursionlimit(pow(10,7))
import collections
from collections import defaultdict,Counter
from statistics import median
input=stdin.readline
# print=stdout.write
from queue import Queue
inf = float("inf")
from operator import neg;
mod=pow(10,9)+7
def fun(l):
 m=[[l[0]]]
 for i in range(1,n):
  if m[-1][-1]==l[i]:
   m[-1]+=[l[i]]
  else:
   m.append([l[i]])
 count=[]
 for i in range(len(m)):
  count.append(len(m[i]))
 return count;
def function(l1,index,prev,count):
 tuple=(index,prev,count)
 if tuple in dict:
  return dict[tuple]
 n=len(l1)
 if index==n:
  return 0;
 if count>=3:
  if index%2==prev:

   a1=l1[index]+function(l1,index+1,prev,count)
   dict[tuple] =a1;
   return a1;
  else:

   dict[tuple]=function(l1,index+1,prev,count);
   return dict[tuple]
 if prev==None:
  skip=function(l1,index+1,prev,count)
  not_skip=l1[index]+function(l1,index+1,index%2,count+1)
  maxa=max(skip,not_skip)
  dict[tuple]=maxa;
  return maxa;

 if index%2==prev:
  dict[tuple]=l1[index]+function(l1,index+1,index%2,count)
  return dict[tuple]
 if index%2!=prev:
  skip=function(l1,index+1,prev,count)
  not_skip=l1[index]+function(l1,index+1,index%2,1+count)
  maxa = max(skip, not_skip)
  dict[tuple]=maxa
  return maxa;

t=int(input())
for i in range(t):
 s=input()
 l=list(s)
 l.pop()
 n=len(l)
 l=[int(i) for i in l]
 l1=fun(l)
 dict=defaultdict(int)
 theta=function(l1,0,None,0)
 print(n-theta)


# cook your dish here
import math;
from math import gcd,sqrt,floor,factorial,ceil
from bisect import bisect_left,bisect_right
import bisect;
import sys;
from sys import stdin,stdout
import os
sys.setrecursionlimit(pow(10,7))
import collections
from collections import defaultdict,Counter
from statistics import median
# input=stdin.readline
# print=stdout.write
from queue import Queue
inf = float("inf")
from operator import neg;
mod=pow(10,9)+7
def fun(l):
 m=[[l[0]]]
 for i in range(1,n):
  if m[-1][-1]==l[i]:
   m[-1]+=[l[i]]
  else:
   m.append([l[i]])
 count=[]
 for i in range(len(m)):
  count.append(len(m[i]))
 return count;
def function(l1,index,prev,count):
 tuple=(index,prev,count)
 if tuple in dict:
  return dict[tuple]
 n=len(l1)
 if index==n:
  return 0;
 if count>=3:
  if index%2==prev:

   a1=l1[index]+function(l1,index+1,prev,count)
   dict[tuple] =a1;
   return a1;
  else:

   dict[tuple]=function(l1,index+1,prev,count);
   return dict[tuple]
 if prev==None:
  skip=function(l1,index+1,prev,count)
  not_skip=l1[index]+function(l1,index+1,index%2,count+1)
  maxa=max(skip,not_skip)
  dict[tuple]=maxa;
  return maxa;

 if index%2==prev:
  dict[tuple]=l1[index]+function(l1,index+1,index%2,count)
  return dict[tuple]
 if index%2!=prev:
  skip=function(l1,index+1,prev,count)
  not_skip=l1[index]+function(l1,index+1,index%2,1+count)
  maxa = max(skip, not_skip)
  dict[tuple]=maxa
  return maxa;

t=int(input())
for i in range(t):
 s=input()
 l=list(s)
 n=len(l)
 l=[int(i) for i in l]
 l1=fun(l)
 dict=defaultdict(int)
 theta=function(l1,0,None,0)
 print(n-theta)


# cook your dish here
t = int(input())
for _ in range(t):
 s = input()
 n = len(s)
 o, z, oz, zo, ozo, zoz = 0,0,0,n,n,n
 for i in s:
  if i=='1':
   zo = min(zo,z)
   z = z+1
   ozo = min(ozo,oz)
   oz = oz+1
   zoz = zoz+1
  else:
   oz = min(oz, o)
   o = o+1
   zoz = min(zoz, zo)
   zo = zo+1
   ozo = ozo+1
 print(min(o, z, oz, zo, ozo, zoz))

# cook your dish here
# code by RAJ BHAVSAR
for _ in range(int(input())):
 s = str(input())
 dp = [0,0,len(s),len(s),len(s),len(s)]
 for i in s:
  if(i == '1'):
   dp[3] = min(dp[3],dp[0])
   dp[0] += 1
   dp[5] = min(dp[5],dp[2])
   dp[2] += 1
   dp[4] += 1
  else:
   dp[2] = min(dp[2],dp[1])
   dp[1] += 1
   dp[4] = min(dp[4],dp[3])
   dp[3] += 1
   dp[5] += 1
 print(min(dp))

for _ in range(int(input())):
 bi = input().strip()
 dp = [0 if i < 2 else len(bi) for i in range(6)]
 for c in bi:
  if c == '1':
   dp[3] = min(dp[3], dp[0])
   dp[0] += 1
   dp[5] = min(dp[5], dp[2])
   dp[2] += 1
   dp[4] += 1
  else:
   dp[2] = min(dp[2], dp[1])
   dp[1] += 1
   dp[4] = min(dp[4], dp[3])
   dp[3] += 1
   dp[5] += 1
 print(min(dp))
   


t = int(input())
while(t>0):
 st = input()
 dp = [0 if(i<2) else len(st) for i in range(6)] # dp is a 6 element array,         where the first two elements signify the no. of ones and no. of zeros         respectively while, the 3rd and 4th element signifies the current 10 or         01 trend and the 5th and 6th element takes care of the 101 or 010 trend
 for c in st:
  if(c=='1'):
   dp[3] = min(dp[3],dp[1])
   dp[1]+=1
   dp[4] = min(dp[4],dp[2])
   dp[2]+=1
   dp[5]+=1
  else:
   dp[2] = min(dp[2],dp[0])
   dp[0]+=1
   dp[5] = min(dp[5],dp[3])
   dp[3]+=1
   dp[4]+=1
 print(min(dp))
 t=t-1


for _ in range(int(input())):
 bi = input().strip()
 dp = [0 if i < 2 else len(bi) for i in range(6)]
 for c in bi:
  if c == '1':
   dp[3] = min(dp[3], dp[0])
   dp[0] += 1
   dp[5] = min(dp[5], dp[2])
   dp[2] += 1
   dp[4] += 1
  else:
   dp[2] = min(dp[2], dp[1])
   dp[1] += 1
   dp[4] = min(dp[4], dp[3])
   dp[3] += 1
   dp[5] += 1
 print(min(dp))


import numpy as np
i8 = np.int64


def solve_core(a, n):
 res = 0
 s1 = a[0]
 s2 = a[1]
 s3 = np.sum(a[2::2])
 for i in range(1, n, 2):
  t3 = s3
  for j in range(i + 1, n + 1, 2):
   res = max(res, s1 + s2 + t3)
   s2 += a[j + 1]
   t3 -= a[j]
  s1 += a[i + 1]
  s2 = a[i + 2]
  s3 -= a[i + 1]
 return res


def solve(S):
 N = len(S)
 a = np.zeros(N + 2, i8)
 i = 0
 prev = S[0]
 count = 0
 for c in S:
  if c == prev:
   count += 1
  else:
   a[i] = count
   prev = c
   count = 1
   i += 1
 else:
  a[i] = count
  i += 1
 if i < 4:
  return 0
 else:
  res = max(solve_core(a, i), solve_core(a[1:], i - 1))
  return N - res

def main():
 T = int(input())
 for _ in range(T):
  S = input()
  print(solve(S))

def __starting_point():
 main()
__starting_point()

T=int(input())
for _ in range(T):
 s=input()
 l=[]
 a=0
 b=0
 for i in s:
  if i=='1':
   if a!=0:
    l.append(a)
    a=0
   b+=1
  else:
   if b!=0:
    l.append(b)
    b=0
   a-=1
 if a!=0:
  l.append(a)
 if b!=0:
  l.append(b)
 A=[0]
 B=[0]
 for i in l:
  if i<0:
   A.append(-i+A[-1])
   B.append(B[-1])
  else:
   A.append(A[-1])
   B.append(i+B[-1])
 m=0
 x=len(A)-1
 for i in range(1,x+1):
  for j in range(i,x+1):
   m=max(m,A[j]-A[i-1]+B[i-1]+B[x]-B[j],B[j]-B[i-1]+A[i-1]+A[x]-A[j])
 print(len(s)-m)


import sys
from random import randint


def rec(x, y, b):
 if x == n:
  return 0
 if y == 3:
  return n
 if dp[x][y] != -1:
  return dp[x][y]
 if y == 1:
  p = b ^ 1
 else:
  p = b
 res = n
 if a[x] != p:
  res = min(res, rec(x, y+1, b))
  res = min(res, 1+rec(x+1, y, b))
 else:
  res = min(res, rec(x+1, y, b))
 dp[x][y] = res
 return dp[x][y]


sys.setrecursionlimit(10**6)
t = int(input())
# t = 1
for _ in range(t):
 a = list(map(int, list(input())))
 # a = [randint(0, 1) for i in range(1000)]
 n = len(a)
 dp = [[-1, -1, -1] for i in range(n)]
 res = rec(0, 0, 0)
 dp = [[-1, -1, -1] for i in range(n)]
 res = min(res, rec(0, 0, 1))
 print(res)