活动执行问题：优先队列模型

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <bitset>
#include <assert.h>

using namespace std;
typedef long long ll;
typedef set<int>::iterator ssii;

#define Cmp(a, b) memcmp(a, b, sizeof(b))
#define Cpy(a, b) memcpy(a, b, sizeof(b))
#define Set(a, v) memset(a, v, sizeof(a))
#define debug(x) cout << #x << ": " << x << endl
#define _forS(i, l, r) for(set<int>::iterator i = (l); i != (r); i++)
#define _rep(i, l, r) for(int i = (l); i <= (r); i++)
#define _for(i, l, r) for(int i = (l); i < (r); i++)
#define _forDown(i, l, r) for(int i = (l); i >= r; i--)
#define debug_(ch, i) printf(#ch"[%d]: %d\n", i, ch[i])
#define debug_m(mp, p) printf(#mp"[%d]: %d\n", p->first, p->second)
#define debugS(str) cout << "dbg: " << str << endl;
#define debugArr(arr, x, y) _for(i, 0, x) { _for(j, 0, y) printf("%c", arr[i][j]); printf("\n"); }
#define _forPlus(i, l, d, r) for(int i = (l); i + d < (r); i++)
#define lowbit(i) (i & (-i))
#define MPR(a, b) make_pair(a, b)

pair<int, int> crack(int n) {
    int st = sqrt(n);
    int fac = n / st;
    while (n % st) {
        st += 1;
        fac = n / st;
    }

    return make_pair(st, fac);
}

inline ll qpow(ll a, int n) {
    ll ans = 1;
    for(; n; n >>= 1) {
        if(n & 1) ans *= 1ll * a;
        a *= a;
    }
    return ans;
}

template <class T>
inline bool chmax(T& a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

ll gcd(ll a, ll b) {
    return b == 0 ? a : gcd(b, a % b);
}

ll ksc(ll a, ll b, ll mod) {
    ll ans = 0;
    for(; b; b >>= 1) {
        if (b & 1) ans = (ans + a) % mod;
        a = (a * 2) % mod;
    }
    return ans;
}

ll ksm(ll a, ll b, ll mod) {
    ll ans = 1 % mod;
    a %= mod;

    for(; b; b >>= 1) {
        if (b & 1) ans = ksc(ans, a, mod);
        a = ksc(a, a, mod);
    }

    return ans;
}

template <class T>
inline bool chmin(T& a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

bool _check(int x) {
    //
    return true;
}

int bsearch1(int l, int r) {
    while (l < r) {
        int mid = (l + r) >> 1;
        if(_check(mid)) r = mid;
        else l = mid + 1;
    }
    return l;
}

int bsearch2(int l, int r) {
    while (l < r) {
        int mid = (l + r + 1) >> 1;
        if(_check(mid)) l = mid;
        else r = mid - 1;
    }
    return l;
}

template<class T>
bool lexSmaller(vector<T> a, vector<T> b) {
    int n = a.size(), m = b.size();
    int i;
    for(i = 0; i < n && i < m; i++) {
        if (a[i] < b[i]) return true;
        else if (b[i] < a[i]) return false;
    }
    return (i == n && i < m);
}

// ============================================================== //

const int Max = 10000000;
const int maxn = 20000;
int n;

class A {
public:
    int l, r, w;
    A() = default;
    A(int l, int r, int w) : l(l), r(r), w(w) {}

    bool operator< (const A &rhs) const {
        return r > rhs.r;
    }
} a[maxn];


inline bool cmp(const A &a, const A &b) {
    return a.l < b.l;
}

bool check(int speed) {
    priority_queue<A> que;

    int i = 1;
    _rep(p, 1, maxn) {
        while (i <= n && a[i].l == p) que.push(a[i++]);

        if (que.empty()) {
            if (i > n) break;
            else continue;
        }

        int tot = speed;
        while (que.size() && tot > 0) {
            A t = que.top(); que.pop();
            if (t.r <= p && t.w > 0) return false;

            if (tot >= t.w) {
                tot -= t.w;
                t.w = 0;
            }
            else {
                t.w -= tot;
                tot = 0;
                que.push(t);
            }
        }
    }
    return que.empty();
}

void solve() {
    sort(a+1, a+1+n, cmp);
    int L = 0, R = Max;
    while (L < R) {
        int mid = (L + R) >> 1;
        if (check(mid)) R = mid;
        else L = mid + 1;
    }
    printf("%d\n", L);
}

void init() {
    //
}

int main() {
    //freopen("input.txt", "r", stdin);
    int kase;
    cin >> kase;

    while (kase--) {
        init();
        scanf("%d", &n);

        _rep(i, 1, n) scanf("%d%d%d", &a[i].l, &a[i].r, &a[i].w);

        // solve
        solve();
    }
}