#include "supertrees.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string; // yay python!
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
#define tcT template<class T
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>;
tcT, size_t SZ> using AR = array<T,SZ>;
// pairs
#define mp make_pair
#define f first
#define s second
// vectors
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18; // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
// helper funcs
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
tcT> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
#define tcTU tcT, class U
tcTU> T fstTrue(T lo, T hi, U f) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
lo --; assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo+1)/2;
f(mid) ? lo = mid : hi = mid-1;
}
return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
auto it = t.find(u); assert(it != end(t));
t.erase(u); } // element that doesn't exist from (multi)set
// INPUT
#define tcTUU tcT, class ...U
tcT> void re(complex<T>& c);
tcTU> void re(pair<T,U>& p);
tcT> void re(vector<T>& v);
tcT, size_t SZ> void re(AR<T,SZ>& a);
tcT> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); }
tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; }
tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
tcT> void re(vector<T>& x) { trav(a,x) re(a); }
tcT, size_t SZ> void re(AR<T,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
return b ? "true" : "false";
#else
return ts((int)b);
#endif
}
tcT> str ts(complex<T> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
tcTU> str ts(pair<T,U> p);
tcT> str ts(T v) { // containers with begin(), end()
#ifdef LOCAL
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
#else
bool fst = 1; str res = "";
for (const auto& x: v) {
if (!fst) res += " ";
fst = 0; res += ts(x);
}
return res;
#endif
}
tcTU> str ts(pair<T,U> p) {
#ifdef LOCAL
return "("+ts(p.f)+", "+ts(p.s)+")";
#else
return ts(p.f)+" "+ts(p.s);
#endif
}
// OUTPUT
tcT> void pr(T x) { cout << ts(x); }
tcTUU> void pr(const T& t, const U&... u) {
pr(t); pr(u...); }
void ps() { pr("\n"); } // print w/ spaces
tcTUU> void ps(const T& t, const U&... u) {
pr(t); if (sizeof...(u)) pr(" "); ps(u...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU> void DBG(const T& t, const U&... u) {
cerr << ts(t); if (sizeof...(u)) cerr << ", ";
DBG(u...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
#define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
<< __FUNCTION__ << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
/**
* Description: Disjoint Set Union with path compression
* and union by size. Add edges and test connectivity.
* Use for Kruskal's or Boruvka's minimum spanning tree.
* Time: O(\alpha(N))
* Source: CSAcademy, KACTL
* Verification: *
*/
struct DSU {
vi e; void init(int N) { e = vi(N,-1); }
int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
bool sameSet(int a, int b) { return get(a) == get(b); }
int size(int x) { return -e[get(x)]; }
bool unite(int x, int y) { // union by size
x = get(x), y = get(y); if (x == y) return 0;
if (e[x] > e[y]) swap(x,y);
e[x] += e[y]; e[y] = x; return 1;
}
};
/**template<class T> T kruskal(int N, vector<pair<T,pi>> ed) {
sort(all(ed));
T ans = 0; DSU D; D.init(N); // edges that unite are in MST
trav(a,ed) if (D.unite(a.s.f,a.s.s)) ans += a.f;
return ans;
}*/
std::vector<std::vector<int>> p;
std::vector<std::vector<int>> b;
vb vis;
vi cur;
int n;
void dfs(int x) {
if (vis[x]) return;
vis[x] = 1;
F0R(i,n) if (p[x][i]) dfs(i);
cur.pb(x);
}
DSU D;
void ae(int x, int y) {
assert(x != y && !b[x][y]);
b[x][y] = b[y][x] = 1;
}
bool go(int x) {
cur.clear();
dfs(x);
trav(a,cur) trav(b,cur) if (!p[a][b]) return 0;
vi cyc;
trav(a,cur) if (D.get(a) == a) {
cyc.pb(a);
vi comp; F0R(i,n) if (D.get(i) == a) comp.pb(i);
trav(x,comp) trav(y,comp) if (p[x][y] != 1) return 0;
FOR(j,1,sz(comp)) ae(comp[0],comp[j]);
}
assert(sz(cyc));
if (sz(cyc) == 2) return 0;
if (sz(cyc) == 1) return 1;
F0R(i,sz(cyc)) ae(cyc[i],cyc[(i+1)%sz(cyc)]);
return 1;
}
int construct(std::vector<std::vector<int>> _p) {
p = _p;
n = p.size(); vis.rsz(n);
F0R(i,n) F0R(j,n) if (p[i][j] == 3) return 0;
D.init(n);
F0R(i,n) F0R(j,n) if (p[i][j] == 1) D.unite(i,j);
b = vector<std::vector<int>>(n,vi(n));
F0R(i,n) if (!vis[i]) {
if (!go(i)) return 0;
}
build(b);
return 1;
// std::vector<std::vector<int>> answer;
// for (int i = 0; i < n; i++) {
// std::vector<int> row;
// row.resize(n);
// answer.push_back(row);
// }
// build(answer);
return 1;
}
