#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <stack>
#include <iomanip>
#include <fstream>
#include <string>
#include <set>
#include <deque>
#include <queue>
#include <map>
#include <bitset>
#include <random>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
#define endl "\n"
#define sqrt sqrtl

#define all(a) a.begin(), a.end();

const ll inf = 1e9 + 13;
long double eps = 1e-9;
const ll maxsz = 1e6 + 5;

void solve() {
    string s;
    ll i, j;
    cin >> s;
    vector <vector <ll> > a(5 + 1);
    vector <vector <ll> > b(5 + 1);
    ll pos1 = 1, pos2 = 1;
    a[0] = { 0 };
    b[0] = { 0 };
    for (i = 0; i < s.size(); i++) {
        if (i % 2 == 0) {
            char t = s[i];
            vector <ll> now;
            for (j = 0; j < a[pos1 - 1].size(); j++) {
                if (t == '0') {
                    now.push_back(a[pos1 - 1][j]);
                }
                else if (t == '1') {
                    now.push_back(a[pos1 - 1][j] + 1);
                }
                else {
                    now.push_back(a[pos1 - 1][j]);
                    now.push_back(a[pos1 - 1][j] + 1);
                }
            }
            a[pos1] = now;
            pos1++;
        }
        else {
            char t = s[i];
            vector <ll> now;
            for (j = 0; j < b[pos2 - 1].size(); j++) {
                if (t == '0') {
                    now.push_back(b[pos2 - 1][j]);
                }
                else if (t == '1') {
                    now.push_back(b[pos2 - 1][j] + 1);
                }
                else {
                    now.push_back(b[pos2 - 1][j]);
                    now.push_back(b[pos2 - 1][j] + 1);
                }
            }
            b[pos2] = now;
            pos2++;
        }
    }
    vector <ll> s1(5 + 1);
    vector <ll> s2(5 + 1);
    for (i = 1; i <= 5; i++) {
        pair <ll, ll> f = { inf,-inf }, s = { inf, -inf };
        for (j = 0; j < a[i].size(); j++) {
            if (a[i][j] < f.first) {
                f.first = a[i][j];
            }
            if (a[i][j] > f.second) {
                f.second = a[i][j];
            }
        }
        for (j = 0; j < b[i].size(); j++) {
            if (b[i][j] < s.first) {
                s.first = b[i][j];
            }
            if (b[i][j] > s.second) {
                s.second = b[i][j];
            }
        }
        if (s2[i - 1] > f.first + ((10 - (2 * i)) / 2)) {
            cout << 2 * i - 1 << endl;
            return;
        }
        if (f.second > s1[i - 1] + ((10 - 2 * i) / 2 + 1)) {
            cout << 2 * i - 1 << endl;
            return;
        }
        if (f.second > s.first + (10 - 2 * i) / 2) {
            cout << 2 * i << endl;
            return;
        }
        if (s.second > f.first + ((10 - 2 * i) / 2)) {
            cout << 2 * i << endl;
            return;
        }
        s1[i] = s.first;
        s2[i] = s.second;
    }
    cout << 10 << endl;
}

signed main() {
#ifdef _DEBUG
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    cout.tie(NULL);
    ll t;
    cin >> t;
    while (t--) solve();
}