#include "supertrees.h"
#include <bits/stdc++.h>

using namespace std;

int construct(std::vector<std::vector<int>> p) {
	int n = p.size();

    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            if (p[i][j] == 3) {
                return 0;
            }
        }
    }

	vector ans(n, vector<int>(n));

    auto addEdge = [&](int x, int y) {
        ans[x][y] = ans[y][x] = true;
    };

    vector<bool> used(n);
    vector<int> treeNum(n, -1), cycleNum(n, -1);
    vector<vector<int>> subtree(n);
    int top = 0;
    vector<int> cyc;

    // generate trees
    for (int i = 0; i < n; ++i) {
        if (!used[i]) {
            vector<int> tree;
            for (int to = i; to < n; ++to) {
                if (!used[to] && p[i][to] == 1) {
                    used[to] = true;
                    tree.push_back(to);
                }
            }
            for (int x : tree) {
                treeNum[x] = top;
            }
            subtree[i] = tree;
            top += 1;
            cyc.push_back(i);
            for (int j = 0; j + 1 < size(tree); ++j) {
                addEdge(tree[j], tree[j + 1]);
            }
        }
    }

    top = 0;
    // generate cycles
    fill(used.begin(), used.end(), false);
    for (int i = 0; i < size(cyc); ++i) {
        if (!used[i]) {
            vector<int> now{cyc[i]};
            used[i] = true;
            for (int j = i + 1; j < size(cyc); ++j) {
                if (!used[j] && p[cyc[i]][cyc[j]] == 2) {
                    used[j] = true;
                    now.push_back(cyc[j]);
                }
            }
            for (int x : now) {
                for (int t : subtree[x]) {
                    cycleNum[t] = top;
                }
            }
            if (size(now) == 2) {
                return 0;
            }
            if (size(now) > 1) {
                for (int j = 0; j < size(now); ++j) {
                    addEdge(now[j], now[(j + 1) % size(now)]);
                }
            }
            top += 1;
        }
    }

    for (int i = 0; i < n; ++i) {
        for (int j = i; j < n; ++j) {
            if (p[i][j] && cycleNum[i] != cycleNum[j] || !p[i][j] && cycleNum[i] == cycleNum[j]) {
                return 0;
            }
            if (cycleNum[i] == cycleNum[j]) {
                if (treeNum[i] == treeNum[j] && p[i][j] == 2 || treeNum[i] != treeNum[j] && p[i][j] == 1) {
                    return 0;
                }
            }
        }
    }

    build(ans);
    return 1;
}