#include "mars.h"
#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pair

using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;

char gr[105][105];
PII rt[105][105];
PII root(PII u) {
    return rt[u.first][u.second] == u ? u : rt[u.first][u.second] = root(rt[u.first][u.second]);
}
int unite(PII u, PII v) {
    u = root(u);
    v = root(v);

    if (u == v)
        return 0;

    rt[v.first][v.second] = u;
    return 1;
}
vector<PII> calc(int l, int b) {
    vector<PII> bpos;
    char pr = '0';

    for (int i = l - 1; i >= b; i --) {
        if (pr == '0' && gr[b][i] == '1')
            bpos.push_back(MP(b, i));

        pr = gr[b][i];
    }

    for (int i = b + 1; i < l; i ++) {
        if (pr == '0' && gr[i][b] == '1')
            bpos.push_back(MP(i, b));

        pr = gr[i][b];
    }

    return bpos;
}
std::string process(std::vector <std::vector<std::string>> a, int i, int j, int k, int n) {
    if (i < 2 * (n - k - 1) && j < 2 * (n - k - 1))
        return a[0][0];

    string ret;

    if (i < 2 * (n - k - 1)) {
        if (k == 0)
            ret = a[0][0][0] + (a[1][0][0] + (a[0][1][0] + (a[1][1][0] + (a[0][2][0] + a[1][2]))));
        else
            ret = a[0][0][0] + (a[1][0][0] + (a[0][1][0] + (a[1][1][0] + a[0][2])));

        ret.resize(100);
        return ret;
    }

    if (j < 2 * (n - k - 1)) {
        if (k == 0)
            ret = a[0][0][0] + (a[0][1][0] + (a[1][0][0] + (a[1][1][0] + (a[2][0][0] + a[2][1]))));
        else
            ret = a[0][0][0] + (a[0][1][0] + (a[1][0][0] + (a[1][1][0] + a[2][0])));

        ret.resize(100);
        return ret;
    }

    if (k == 0) {
        rep(u, 3) rep(v, 3) gr[u][v] = a[u][v][0];
    } else {
        rep(u, 3) rep(v, 3) gr[u][v] = a[u][v][0];
        int pos;
        rep(t, 2) {
            pos = 0;

            for (int v = 2; v < 2 * n + 1 - j; v ++)
                rep(u, 2) gr[t + u][v] = a[t][2][pos ++];
        }
        rep(t, 2) {
            pos = 0;

            for (int v = 2; v < 2 * n + 1 - i; v ++)
                rep(u, 2) gr[v][t + u] = a[2][t][pos ++];
        }
    }

    int l = 2 * n + 1 - i, cnt = 0;
    vector<PII> bpos = calc(l, 2);
    vector<int> sta;
    rep(u, 10) cnt |= (a[2][2][u] == '1') << u;

    rep(u, l) rep(v, l) rt[u][v] = MP(u, v);
    rep(u, bpos.size()) {
        if (a[2][2][u * 2 + 10] == '0')
            sta.push_back(u);

        rt[bpos[u].first][bpos[u].second] = bpos[sta.back()];

        if (a[2][2][u * 2 + 11] == '0')
            sta.pop_back();

        cnt --;
    }

    rep(u, l) rep(v, l) if ((u <= 2 || v <= 2) && gr[u][v] == '1') {
        cnt ++;

        if (u > 0 && gr[u - 1][v] == '1')
            cnt -= unite(MP(u, v), MP(u - 1, v));

        if (v > 0 && gr[u][v - 1] == '1')
            cnt -= unite(MP(u, v), MP(u, v - 1));
    }

    rep(u, l) rep(v, l) if (u <= 2 || v <= 2)
        root(MP(u, v));

    ret = string(100, '0');
    rep(u, 10) ret[u] = '0' + (cnt >> u & 1);

    if (i == 0)
        return ret;

    bpos = calc(l, 0);
    rep(u, bpos.size()) {

        rep(v, u) if (rt[bpos[v].first][bpos[v].second] == rt[bpos[u].first][bpos[u].second])
            ret[u * 2 + 10] = '1';

        for (int v = u + 1; v < (int)bpos.size(); v ++)
            if (rt[bpos[v].first][bpos[v].second] == rt[bpos[u].first][bpos[u].second])
                ret[u * 2 + 11] = '1';
    }
    return ret;
}