Problem:
Score: 600 points

Problem Statement

There is a grass field that stretches infinitely.

In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).

There are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).

What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.

Constraints

All values in input are integers between -10^9 and 10^9 (inclusive).

1 \leq N, M \leq 1000

A_i < B_i\ (1 \leq i \leq N)

E_j < F_j\ (1 \leq j \leq M)

The point (0, 0) does not lie on any of the given segments.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1 C_1
:
A_N B_N C_N
D_1 E_1 F_1
:
D_M E_M F_M

Output

If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in \mathrm{cm^2}.

(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)

Sample Input 1

5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4

Sample Output 1

13

The area of the region the cow can reach is 13\ \mathrm{cm^2}.

Sample Input 2

6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4

Sample Output 2

INF

The area of the region the cow can reach is infinite.

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#line 2 "header.hpp"

//%snippet.set('header')%
//%snippet.fold()%
#ifndef HEADER_H
#define HEADER_H

// template version 2.0
using namespace std;
#include <bits/stdc++.h>
#include<bits/stdc++.h>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <cctype>
#include <string>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <functional>

// varibable settings
const long long INF = 1e18;
template <class T> constexpr T inf = numeric_limits<T>::max() / 2.1;

#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__)
#define _rrep(i, n) rrepi(i, 0, n)
#define rrepi(i, a, b) for (ll i = (ll)((b)-1); i >= (ll)(a); --i)
#define r_rep(...) _overload3(__VA_ARGS__, rrepi, _rrep, )(__VA_ARGS__)
#define each(i, a) for (auto &&i : a)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define mt(...) make_tuple(__VA_ARGS__)
#define ub upper_bound
#define lb lower_bound
#define lpos(A, x) (lower_bound(all(A), x) - A.begin())
#define upos(A, x) (upper_bound(all(A), x) - A.begin())
template <class T> inline void chmax(T &a, const T &b) { if ((a) < (b)) (a) = (b); }
template <class T> inline void chmin(T &a, const T &b) { if ((a) > (b)) (a) = (b); }
template <typename X, typename T> auto make_table(X x, T a) { return vector<T>(x, a); }
template <typename X, typename Y, typename Z, typename... Zs> auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return vector<decltype(cont)>(x, cont); }

#define divceil(a, b) ((a) + (b)-1) / (b)
#define is_in(x, a, b) ((a) <= (x) && (x) < (b))
#define uni(x) sort(all(x)); x.erase(unique(all(x)), x.end())
#define slice(l, r) substr(l, r - l)

typedef long long ll;
typedef long double ld;

template <typename T>
using PQ = priority_queue<T, vector<T>, greater<T>>;
struct Fast { Fast() { std::cin.tie(0); ios::sync_with_stdio(false); } } fast;
void check_input() { assert(cin.eof() == 0); int tmp; cin >> tmp; assert(cin.eof() == 1); }

#if defined(PCM) || defined(LOCAL)
#else
#define dump(...) ;
#define dump_1d(...) ;
#define dump_2d(...) ;
#define cerrendl ;
#endif

#endif /* HEADER_H */
//%snippet.end()%
#line 2 "solve.cpp"
template<class T=ll> using vec = vector<T>;

struct zipper {                             /*{{{*/
    unordered_map<long long, int> zip_map;  // [2:0, 3:1, 5:2, 10:3] debugしづらい
    // map<long long, int> zip_map;  // [2:0, 3:1, 5:2, 10:3]
    vector<long long> _unzipper;            // [2, 3, 5, 10]
    bool _is_build = false;
    int n = 0;

    zipper(long long inf_value = INF) { /*{{{*/
        _unzipper.push_back(-inf_value);
        _unzipper.push_back(inf_value);
    }                                                        /*}}}*/
    zipper(vector<long long> a, long long inf_value = INF) { /*{{{*/
        _unzipper = vector<long long>(sz(a));
        rep(i, sz(a)) { _unzipper[i] = a[i]; }
        _unzipper.push_back(-inf_value);
        _unzipper.push_back(inf_value);
        build();
    }                              /*}}}*/
    void add_value(long long lv) { /*{{{*/
        _unzipper.push_back(lv);
        _is_build = false;
    }              /*}}}*/
    void build() { /*{{{*/
        uni(_unzipper);
        zip_map.clear();
        n = sz(_unzipper);
        rep(i, n) { zip_map[_unzipper[i]] = i; }
        _is_build = true;
    }                              /*}}}*/
    vector<int> zip(vector<long long> lvs) { /*{{{*/
        if (!_is_build) assert(false);
        int n = sz(lvs);
        vector<int> res(n);
        rep(i, n) res[i] = zip_map[lvs[i]];
        return res;
    }                              /*}}}*/
    int zip(long long lv) { /*{{{*/
        if (!_is_build) assert(false);
        return zip_map[lv];
    }                                               /*}}}*/
    int operator()(long long lv) { return zip(lv); }

    long long unzip(int sv) { /*{{{*/
        if (!_is_build) assert(false);
        return _unzipper[sv];
    }                              /*}}}*/
    int operator[](int sv) { return unzip(sv); }

    int size() {return n;}

#if defined(PCM) || defined(LOCAL) /*{{{*/
    friend ostream& operator<<(ostream& os, const zipper& zp) {
        os << endl;
        os << "_is_build: " << zp._is_build << endl;
        os << "zip_map:   " << zp.zip_map << endl;
        os << "_unzipper:   " << zp._unzipper << endl;
        return os;
    }
#endif /*}}}*/
};     /*}}}*/
// How to use {{{
// construct
// auto z = zipper(x); // x: vector<long long>;
// auto z = zipper(x, 30*INF);

// auto z = zipper();
// auto z = zipper();
// z.add_value(3);
// z.add_value(5);
// z.add_value(10);
// z.add_value(100000000);
// z.build();

// other method
// z(x[i]); -> zipped x[i]
// z.unzip(z(x[i])) -> x[i];
// z.get_zipped(x) -> zipped x
// }}}

int solve() {
    ll n,m;cin>>n>>m;/*{{{*/
    vec<ll> a(n), b(n), c(n);
    zipper zx;
    zx.add_value(0);
    zipper zy;
    zy.add_value(0);

    rep(i, n){
        cin>>a[i]>>b[i]>>c[i];
        zx.add_value(a[i]);
        zx.add_value(b[i]);
        zy.add_value(c[i]);
    }

    vec<ll> d(m), e(m), f(m);
    rep(i, m){
        cin>>d[i]>>e[i]>>f[i];
        zx.add_value(d[i]);
        zy.add_value(e[i]);
        zy.add_value(f[i]);
    }
    zx.build();
    zy.build();/*}}}*/

    ll h = sz(zx);
    ll w = sz(zy);
    auto nid = [&](int i, int j){return (i*w + j);};
    int di[] = {1, -1, 0, 0};
    int dj[] = {0, 0, 1, -1};

    vec<vec<ll>> kinshi(h*w);
    rep(i, n){
        ll za = zx(a[i]);
        ll zb = zx(b[i]);
        rep(r, za, zb){
            ll zc = zy(c[i]);
            kinshi[nid(r, zc)].pb(nid(r, zc-1));
            kinshi[nid(r, zc-1)].pb(nid(r, zc));
        }
    }
    rep(i, m){
        ll ze = zy(e[i]);
        ll zf = zy(f[i]);
        rep(c, ze, zf){
            ll zr = zx(d[i]);
            kinshi[nid(zr, c)].pb(nid(zr-1, c));
            kinshi[nid(zr-1, c)].pb(nid(zr, c));
        }
    }

    ll ans = 0;
    ll x0 = zx(0);
    ll y0 = zy(0);
    stack<pair<ll, ll>> st;
    st.push(mp(x0, y0));
    auto ok = [&](vec<ll>& p, ll x){
        each(el, p){
            if (el==x) return false;
        }
        return true;
    };

    vec<ll> used(h*w);
    while(!st.empty()){
        auto [x, y] = st.top();st.pop();
        if (used[nid(x, y)]) continue;
        used[nid(x, y)] = 1;

        ll dx = zx.unzip(x+1) - zx.unzip(x);
        ll dy = zy.unzip(y+1) - zy.unzip(y);
        ans += dx * dy;

        rep(dir, 4){
            ll nx = x + di[dir];
            ll ny = y + dj[dir];
            if (is_in(nx, 0, h) && is_in(ny, 0, w)){
                if (ok(kinshi[nid(x, y)], nid(nx, ny))){
                    if (nx==0 || nx==h-1 || ny==0 || ny==w-1){
                        cout << "INF" << endl;
                        return 0;
                    }
                    st.push(mp(nx, ny));
                }
            }
        }
    }
    cout << ans << endl;

    return 0; 
}


int main(){/*{{{*/
    solve();
    check_input();
    return 0;
}/*}}}*/