Shubham has a binary string s. A binary string is a string containing only characters "0" and "1".

He can perform the following operation on the string any amount of times: 

  * Select an index of the string, and flip the character at that index. This means, if the character was "0", it becomes "1", and vice versa. 



A string is called good if it does not contain "010" or "101" as a subsequence — for instance, "1001" contains "101" as a subsequence, hence it is not a good string, while "1000" doesn't contain neither "010" nor "101" as subsequences, so it is a good string.

What is the minimum number of operations he will have to perform, so that the string becomes good? It can be shown that with these operations we can make any string good.

A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.

Input

The first line of the input contains a single integer t (1≤ t ≤ 100) — the number of test cases.

Each of the next t lines contains a binary string s (1 ≤ |s| ≤ 1000).

Output

For every string, output the minimum number of operations required to make it good.

Example

Input


7
001
100
101
010
0
1
001100


Output


0
0
1
1
0
0
2

Note

In test cases 1, 2, 5, 6 no operations are required since they are already good strings.

For the 3rd test case: "001" can be achieved by flipping the first character — and is one of the possible ways to get a good string.

For the 4th test case: "000" can be achieved by flipping the second character — and is one of the possible ways to get a good string.

For the 7th test case: "000000" can be achieved by flipping the third and fourth characters — and is one of the possible ways to get a good string.
import java.io.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;



/**
 * *****Virtual contest div1 participate and up solve, cover 3-5 questions.
 * You need to do that for 30 plus such contests before 30 June. Till then only codeforces.*****
 * Another strategy do 15 contest solve at least 3 question each
 * Redo these 15 contest solve remaining, take test again solve :- already solved and unsolved, revision plus learning
 * 90 question in 30 days is good
 * ****Use pen and paper************* check few examples analyze them, some not given in sample also analyze then code
 * Use pen and paper. Solve on paper then code.
 * If there is some reasoning e.g. sequence/paths, try printing first 100 elements or 100 answers using brute and observe.
 * *********Read question with extreme caution. Mistake is happening here which costs time, WA and easy problem not getting solved.*********
 * Sometimes we make question complex due to misunderstanding.
 * Prefix sum and suffix sum is highly usable concept, look for it.
 * Think of cleanest approach. If too many if else are coming then its indication of WA.
 * Solve 1-2 more questions than you solved during contest.
 */
public class Codeforces {

	public static void main(String args[]) throws IOException {
//		Reader in = new Reader();
		FastReader in = new FastReader();//use in case of reading strings
		int t = in.nextInt();
		while (t-->0) {
			String s = in.next();
			int n = s.length();
			if (n == 1) {
				System.out.println(0);
				continue;
			}
			int pz[] = new int[n];
			int po[] = new int[n];
			pz[0] = s.charAt(0) == '0' ? 1 : 0;
			po[0] = 1-pz[0];
			for (int i=1;i<n;i++) {
				char ch = s.charAt(i);
				pz[i] = pz[i-1] + ((ch == '0') ? 1 : 0);
				po[i] = po[i-1] + ((ch == '1') ? 1 : 0);
			}
			int min = Integer.MAX_VALUE, l = 0;
			while (l<n) {
				//10
				int oneToRight = po[n-1]-po[l];
				int zeroToLeft = pz[l];
				min = Math.min(min, oneToRight+zeroToLeft);
				//01
				int zeroToRight = pz[n-1]-pz[l];
				int oneToLeft = po[l];
				min = Math.min(min, zeroToRight+oneToLeft);
				l++;
			}
			System.out.println(min);
		}
		in.close();
	}

	static class Pair {
		Long x;
		Long y;
		private Pair(long x, long y) {
			this.x = x;
			this.y = y;
		}
		
		@Override
		public boolean equals(Object o) {
			if (o == null || !(o instanceof Pair))
				return false;
			Pair cor = (Pair)o;
			return x.equals(cor.x) && y.equals(cor.y);
		}
		
		@Override
		public int hashCode() {
			int result = 17;
			return result;
		}
		
		static class PairComparatorX implements Comparator<Pair> {

			@Override
			public int compare(Pair o1, Pair o2) {
				return o1.x.compareTo(o2.x);
			}
			
		}

		static class PairComparatorY implements Comparator<Pair> {

			@Override
			public int compare(Pair o1, Pair o2) {
				return o1.y.compareTo(o2.y);
			}
			
		}

	}
	
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead;
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
        
    } 
	
	private static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public void close() {
			// TODO Auto-generated method stub
			
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

}