Consider a simplified penalty phase at the end of a football match.

A penalty phase consists of at most 10 kicks, the first team takes the first kick, the second team takes the second kick, then the first team takes the third kick, and so on. The team that scores more goals wins; if both teams score the same number of goals, the game results in a tie (note that it goes against the usual football rules). The penalty phase is stopped if one team has scored more goals than the other team could reach with all of its remaining kicks. For example, if after the 7-th kick the first team has scored 1 goal, and the second team has scored 3 goals, the penalty phase ends — the first team cannot reach 3 goals.

You know which player will be taking each kick, so you have your predictions for each of the 10 kicks. These predictions are represented by a string s consisting of 10 characters. Each character can either be 1, 0, or ?. This string represents your predictions in the following way:

  * if s_i is 1, then the i-th kick will definitely score a goal; 
  * if s_i is 0, then the i-th kick definitely won't score a goal; 
  * if s_i is ?, then the i-th kick could go either way. 



Based on your predictions, you have to calculate the minimum possible number of kicks there can be in the penalty phase (that means, the earliest moment when the penalty phase is stopped, considering all possible ways it could go). Note that the referee doesn't take into account any predictions when deciding to stop the penalty phase — you may know that some kick will/won't be scored, but the referee doesn't.

Input

The first line contains one integer t (1 ≤ t ≤ 1 000) — the number of test cases.

Each test case is represented by one line containing the string s, consisting of exactly 10 characters. Each character is either 1, 0, or ?.

Output

For each test case, print one integer — the minimum possible number of kicks in the penalty phase.

Example

Input


4
1?0???1001
1111111111
??????????
0100000000


Output


7
10
6
9

Note

Consider the example test:

In the first test case, consider the situation when the 1-st, 5-th and 7-th kicks score goals, and kicks 2, 3, 4 and 6 are unsuccessful. Then the current number of goals for the first team is 3, for the second team is 0, and the referee sees that the second team can score at most 2 goals in the remaining kicks. So the penalty phase can be stopped after the 7-th kick.

In the second test case, the penalty phase won't be stopped until all 10 kicks are finished.

In the third test case, if the first team doesn't score any of its three first kicks and the second team scores all of its three first kicks, then after the 6-th kick, the first team has scored 0 goals and the second team has scored 3 goals, and the referee sees that the first team can score at most 2 goals in the remaining kicks. So, the penalty phase can be stopped after the 6-th kick.

In the fourth test case, even though you can predict the whole penalty phase, the referee understands that the phase should be ended only after the 9-th kick.
//package contest.HarbourSpaceScholarshipContest;

import java.io.*;
import java.util.*;

/***********************
 * @oj: codeforces
 * @id: hitwanyang
 * @email: 296866643@qq.com
 * @date: 2021/7/22 23:39
 * @url: https://codeforc.es/contest/1553/problem/C
 ***********************/

public class C1553 {
    InputStream  is;
    FastWriter   out;
    String       INPUT = "";

    //提交时注意需要注释掉首行package
    //基础类型数组例如long[]使用Arrays排序容易TLE,可以替换成Long[]
    //int 最大值2**31-1,2147483647;
    //尽量使用long类型,避免int计算的数据溢出
    List<String> total = new ArrayList<>();

    void solve() {
        int t = ni();
        solve("??????????", 0, "", total);
        for (; t > 0; t--)
            go();
    }

    void go() {
        String s = ns();
        char[] ss = s.toCharArray();
        List<String> list = new ArrayList<>();
        for (String x : total) {
            boolean flag = true;
            char[] tmp = x.toCharArray();
            for (int i = 0; i < 10; i++) {
                if (ss[i] != '?' && tmp[i] != ss[i]) {
                    flag = false;
                    break;
                }
            }
            if (flag) {
                list.add(x);
            }
        }
        int ans = 10;
        for (String score : list) {
            char[] tmp = score.toCharArray();
            int even = 0, odd = 0;
            for (int i = 0; i < 10; i++) {
                if (i % 2 == 0 && tmp[i] == '1') {
                    even++;
                }
                if (i % 2 == 1 && tmp[i] == '1') {
                    odd++;
                }
                int x = even, y = even + 5 - i / 2 - 1;
                int m = odd, n = odd + 5 - (i + 1) / 2;
                if (m > y || n < x) {
                    ans = Math.min(ans, i + 1);
                }
            }
        }
        out.println(ans);
    }

    void solve(String x, int index, String res, List<String> list) {
        char[] t = x.toCharArray();
        for (int i = index; i < t.length; i++) {
            if (t[i] == '?') {
                solve(x, i + 1, res + "0", list);
                solve(x, i + 1, res + "1", list);
            } else {
                solve(x, i + 1, res + t[i], list);
            }
        }
        if (res.length() == 10) {
            list.add(res);
        }
    }

    void run() throws Exception {
        is = System.in;
        out = new FastWriter(System.out);

        long s = System.currentTimeMillis();
        solve();
        out.flush();
        //debug log
        //tr(System.currentTimeMillis() - s + "ms");
    }

    public static void main(String[] args) throws Exception {
        new C1553().run();
    }

    private byte[] inbuf  = new byte[1024];
    public int     lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1)
            throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0)
                return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b))
            ;
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private Integer[] na(int n) {
        Integer[] a = new Integer[n];
        for (int i = 0; i < n; i++)
            a[i] = ni();
        return a;
    }

    private Long[] nal(int n) {
        Long[] a = new Long[n];
        for (int i = 0; i < n; i++)
            a[i] = nl();
        return a;
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++)
            map[i] = ns(m);
        return map;
    }

    private Integer[][] nmi(int n, int m) {
        Integer[][] map = new Integer[n][];
        for (int i = 0; i < n; i++)
            map[i] = na(m);
        return map;
    }

    private int ni() {
        return (int) nl();
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
            ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    public static class FastWriter {
        private static final int   BUF_SIZE = 1 << 13;
        private final byte[]       buf      = new byte[BUF_SIZE];
        private final OutputStream out;
        private int                ptr      = 0;

        private FastWriter() {
            out = null;
        }

        public FastWriter(OutputStream os) {
            this.out = os;
        }

        public FastWriter(String path) {
            try {
                this.out = new FileOutputStream(path);
            } catch (FileNotFoundException e) {
                throw new RuntimeException("FastWriter");
            }
        }

        public FastWriter write(byte b) {
            buf[ptr++] = b;
            if (ptr == BUF_SIZE)
                innerflush();
            return this;
        }

        public FastWriter write(char c) {
            return write((byte) c);
        }

        public FastWriter write(char[] s) {
            for (char c : s) {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE)
                    innerflush();
            }
            return this;
        }

        public FastWriter write(String s) {
            s.chars().forEach(c -> {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE)
                    innerflush();
            });
            return this;
        }

        private static int countDigits(int l) {
            if (l >= 1000000000)
                return 10;
            if (l >= 100000000)
                return 9;
            if (l >= 10000000)
                return 8;
            if (l >= 1000000)
                return 7;
            if (l >= 100000)
                return 6;
            if (l >= 10000)
                return 5;
            if (l >= 1000)
                return 4;
            if (l >= 100)
                return 3;
            if (l >= 10)
                return 2;
            return 1;
        }

        public FastWriter write(int x) {
            if (x == Integer.MIN_VALUE) {
                return write((long) x);
            }
            if (ptr + 12 >= BUF_SIZE)
                innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        private static int countDigits(long l) {
            if (l >= 1000000000000000000L)
                return 19;
            if (l >= 100000000000000000L)
                return 18;
            if (l >= 10000000000000000L)
                return 17;
            if (l >= 1000000000000000L)
                return 16;
            if (l >= 100000000000000L)
                return 15;
            if (l >= 10000000000000L)
                return 14;
            if (l >= 1000000000000L)
                return 13;
            if (l >= 100000000000L)
                return 12;
            if (l >= 10000000000L)
                return 11;
            if (l >= 1000000000L)
                return 10;
            if (l >= 100000000L)
                return 9;
            if (l >= 10000000L)
                return 8;
            if (l >= 1000000L)
                return 7;
            if (l >= 100000L)
                return 6;
            if (l >= 10000L)
                return 5;
            if (l >= 1000L)
                return 4;
            if (l >= 100L)
                return 3;
            if (l >= 10L)
                return 2;
            return 1;
        }

        public FastWriter write(long x) {
            if (x == Long.MIN_VALUE) {
                return write("" + x);
            }
            if (ptr + 21 >= BUF_SIZE)
                innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        public FastWriter write(double x, int precision) {
            if (x < 0) {
                write('-');
                x = -x;
            }
            x += Math.pow(10, -precision) / 2;
            //		if(x < 0){ x = 0; }
            write((long) x).write(".");
            x -= (long) x;
            for (int i = 0; i < precision; i++) {
                x *= 10;
                write((char) ('0' + (int) x));
                x -= (int) x;
            }
            return this;
        }

        public FastWriter writeln(char c) {
            return write(c).writeln();
        }

        public FastWriter writeln(int x) {
            return write(x).writeln();
        }

        public FastWriter writeln(long x) {
            return write(x).writeln();
        }

        public FastWriter writeln(double x, int precision) {
            return write(x, precision).writeln();
        }

        public FastWriter write(int... xs) {
            boolean first = true;
            for (int x : xs) {
                if (!first)
                    write(' ');
                first = false;
                write(x);
            }
            return this;
        }

        public FastWriter write(long... xs) {
            boolean first = true;
            for (long x : xs) {
                if (!first)
                    write(' ');
                first = false;
                write(x);
            }
            return this;
        }

        public FastWriter writeln() {
            return write((byte) '\n');
        }

        public FastWriter writeln(int... xs) {
            return write(xs).writeln();
        }

        public FastWriter writeln(long... xs) {
            return write(xs).writeln();
        }

        public FastWriter writeln(char[] line) {
            return write(line).writeln();
        }

        public FastWriter writeln(char[]... map) {
            for (char[] line : map)
                write(line).writeln();
            return this;
        }

        public FastWriter writeln(String s) {
            return write(s).writeln();
        }

        private void innerflush() {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException e) {
                throw new RuntimeException("innerflush");
            }
        }

        public void flush() {
            innerflush();
            try {
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException("flush");
            }
        }

        public FastWriter print(byte b) {
            return write(b);
        }

        public FastWriter print(char c) {
            return write(c);
        }

        public FastWriter print(char[] s) {
            return write(s);
        }

        public FastWriter print(String s) {
            return write(s);
        }

        public FastWriter print(int x) {
            return write(x);
        }

        public FastWriter print(long x) {
            return write(x);
        }

        public FastWriter print(double x, int precision) {
            return write(x, precision);
        }

        public FastWriter println(char c) {
            return writeln(c);
        }

        public FastWriter println(int x) {
            return writeln(x);
        }

        public FastWriter println(long x) {
            return writeln(x);
        }

        public FastWriter println(double x, int precision) {
            return writeln(x, precision);
        }

        public FastWriter print(int... xs) {
            return write(xs);
        }

        public FastWriter print(long... xs) {
            return write(xs);
        }

        public FastWriter println(int... xs) {
            return writeln(xs);
        }

        public FastWriter println(long... xs) {
            return writeln(xs);
        }

        public FastWriter println(char[] line) {
            return writeln(line);
        }

        public FastWriter println(char[]... map) {
            return writeln(map);
        }

        public FastWriter println(String s) {
            return writeln(s);
        }

        public FastWriter println() {
            return writeln();
        }
    }

    public void trnz(int... o) {
        for (int i = 0; i < o.length; i++)
            if (o[i] != 0)
                System.out.print(i + ":" + o[i] + " ");
        System.out.println();
    }

    // print ids which are 1
    public void trt(long... o) {
        Queue<Integer> stands = new ArrayDeque<>();
        for (int i = 0; i < o.length; i++) {
            for (long x = o[i]; x != 0; x &= x - 1)
                stands.add(i << 6 | Long.numberOfTrailingZeros(x));
        }
        System.out.println(stands);
    }

    public void tf(boolean... r) {
        for (boolean x : r)
            System.out.print(x ? '#' : '.');
        System.out.println();
    }

    public void tf(boolean[]... b) {
        for (boolean[] r : b) {
            for (boolean x : r)
                System.out.print(x ? '#' : '.');
            System.out.println();
        }
        System.out.println();
    }

    public void tf(long[]... b) {
        if (INPUT.length() != 0) {
            for (long[] r : b) {
                for (long x : r) {
                    for (int i = 0; i < 64; i++) {
                        System.out.print(x << ~i < 0 ? '#' : '.');
                    }
                }
                System.out.println();
            }
            System.out.println();
        }
    }

    public void tf(long... b) {
        if (INPUT.length() != 0) {
            for (long x : b) {
                for (int i = 0; i < 64; i++) {
                    System.out.print(x << ~i < 0 ? '#' : '.');
                }
            }
            System.out.println();
        }
    }

    private void tr(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
}
