#include <bits/stdc++.h>
#pragma GCC optimize(2)
using namespace std;
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3fLL;
const double PI = acos(-1.0);
const long double eps = 1e-8;
const int mod = 998244353;
const int maxn = 2e5 + 100;
const int N = 3e4 + 100;
const int M = 1e5 + 10;
const long long mm = (1LL << 32);
template <class T>
inline void read(T &x) {
  x = 0;
  char c = getchar();
  bool f = 0;
  for (; !isdigit(c); c = getchar()) f ^= c == '-';
  for (; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  x = f ? -x : x;
}
template <class T>
inline void write(T x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  T y = 1;
  int len = 1;
  for (; y <= x / 10; y *= 10) ++len;
  for (; len; --len, x %= y, y /= 10) putchar(x / y + 48);
}
long long qpow(long long a, long long b, long long mod) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = (ans * a) % mod;
    b >>= 1;
    a = (a * a) % mod;
  }
  return ans;
}
struct Edge {
  int from, to;
  long long cap, flow;
  Edge(int u, int v, long long c, long long f)
      : from(u), to(v), cap(c), flow(f) {}
};
struct Dinic {
  int n, m, s, t;
  vector<Edge> edges;
  vector<int> G[N];
  bool vis[N];
  int d[N];
  int cur[N];
  void init(int n) {
    this->n = n;
    for (int i = 0; i < n; ++i) G[i].clear();
    edges.clear();
  }
  void AddEdge(int from, int to, long long cap) {
    edges.push_back({from, to, cap, 0});
    edges.push_back({to, from, 0, 0});
    m = edges.size();
    G[from].push_back(m - 2);
    G[to].push_back(m - 1);
  }
  bool BFS() {
    memset(vis, 0, sizeof(vis));
    memset(d, 0, sizeof(d));
    queue<int> q;
    q.push(s);
    d[s] = 0;
    vis[s] = 1;
    while (!q.empty()) {
      int x = q.front();
      q.pop();
      for (int i = 0; i < G[x].size(); ++i) {
        Edge &e = edges[G[x][i]];
        if (!vis[e.to] && e.cap > e.flow) {
          vis[e.to] = true;
          d[e.to] = d[x] + 1;
          q.push(e.to);
        }
      }
    }
    return vis[t];
  }
  long long DFS(int x, long long a) {
    if (x == t || a == 0) return a;
    long long flow = 0, f;
    for (int &i = cur[x]; i < G[x].size(); ++i) {
      Edge &e = edges[G[x][i]];
      if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0) {
        e.flow += f;
        edges[G[x][i] ^ 1].flow -= f;
        flow += f;
        a -= f;
        if (a == 0) break;
      }
    }
    return flow;
  }
  long long Maxflow(int s, int t) {
    this->s = s, this->t = t;
    long long flow = 0;
    while (BFS()) {
      memset(cur, 0, sizeof(cur));
      flow += DFS(s, INF);
    }
    return flow;
  }
} mf;
int n, m;
int U[M], V[M], W[M];
bool check(int x) {
  mf.init(2 * n + 5);
  int S = 0, T = 2 * n + 1;
  for (int i = 1; i <= n; ++i) mf.AddEdge(S, i, 1);
  for (int i = 1; i <= n; ++i) mf.AddEdge(n + i, T, 1);
  for (int i = 1; i <= m; ++i) {
    int u = U[i], v = V[i], w = W[i];
    if (w <= x) {
      mf.AddEdge(u, v + n, 1);
    }
  }
  return mf.Maxflow(S, T) == (long long)n;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int i = 1; i <= m; ++i) {
    cin >> U[i] >> V[i] >> W[i];
  }
  int l = 1, r = 1e9, ans = -1;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (check(mid))
      ans = mid, r = mid - 1;
    else
      l = mid + 1;
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

The pandemic is upon us, and the world is in shortage of the most important resource: toilet paper. As one of the best prepared nations for this crisis, BubbleLand promised to help all other world nations with this valuable resource. To do that, the country will send airplanes to other countries carrying toilet paper.

In BubbleLand, there are N toilet paper factories, and N airports. Because of how much it takes to build a road, and of course legal issues, every factory must send paper to only one airport, and every airport can only take toilet paper from one factory.

Also, a road can't be built between all airport-factory pairs, again because of legal issues. Every possible road has number d given, number of days it takes to build that road.

Your job is to choose N factory-airport pairs, such that if the country starts building all roads at the same time, it takes the least amount of days to complete them.

Input

The first line contains two integers N (1 ≤ N ≤ 10^4) - number of airports/factories, and M (1 ≤ M ≤ 10^5) - number of available pairs to build a road between.

On next M lines, there are three integers u, v (1 ≤ u,v ≤ N), d (1 ≤ d ≤ 10^9) - meaning that you can build a road between airport u and factory v for d days.

Output

If there are no solutions, output -1. If there exists a solution, output the minimal number of days to complete all roads, equal to maximal d among all chosen roads.

Example

Input


3 5
1 2 1
2 3 2
3 3 3
2 1 4
2 2 5


Output


4

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize(2)
using namespace std;
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3fLL;
const double PI = acos(-1.0);
const long double eps = 1e-8;
const int mod = 998244353;
const int maxn = 2e5 + 100;
const int N = 3e4 + 100;
const int M = 1e5 + 10;
const long long mm = (1LL << 32);
template <class T>
inline void read(T &x) {
  x = 0;
  char c = getchar();
  bool f = 0;
  for (; !isdigit(c); c = getchar()) f ^= c == '-';
  for (; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
  x = f ? -x : x;
}
template <class T>
inline void write(T x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  T y = 1;
  int len = 1;
  for (; y <= x / 10; y *= 10) ++len;
  for (; len; --len, x %= y, y /= 10) putchar(x / y + 48);
}
long long qpow(long long a, long long b, long long mod) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = (ans * a) % mod;
    b >>= 1;
    a = (a * a) % mod;
  }
  return ans;
}
struct Edge {
  int from, to;
  long long cap, flow;
  Edge(int u, int v, long long c, long long f)
      : from(u), to(v), cap(c), flow(f) {}
};
struct Dinic {
  int n, m, s, t;
  vector<Edge> edges;
  vector<int> G[N];
  bool vis[N];
  int d[N];
  int cur[N];
  void init(int n) {
    this->n = n;
    for (int i = 0; i < n; ++i) G[i].clear();
    edges.clear();
  }
  void AddEdge(int from, int to, long long cap) {
    edges.push_back({from, to, cap, 0});
    edges.push_back({to, from, 0, 0});
    m = edges.size();
    G[from].push_back(m - 2);
    G[to].push_back(m - 1);
  }
  bool BFS() {
    memset(vis, 0, sizeof(vis));
    memset(d, 0, sizeof(d));
    queue<int> q;
    q.push(s);
    d[s] = 0;
    vis[s] = 1;
    while (!q.empty()) {
      int x = q.front();
      q.pop();
      for (int i = 0; i < G[x].size(); ++i) {
        Edge &e = edges[G[x][i]];
        if (!vis[e.to] && e.cap > e.flow) {
          vis[e.to] = true;
          d[e.to] = d[x] + 1;
          q.push(e.to);
        }
      }
    }
    return vis[t];
  }
  long long DFS(int x, long long a) {
    if (x == t || a == 0) return a;
    long long flow = 0, f;
    for (int &i = cur[x]; i < G[x].size(); ++i) {
      Edge &e = edges[G[x][i]];
      if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0) {
        e.flow += f;
        edges[G[x][i] ^ 1].flow -= f;
        flow += f;
        a -= f;
        if (a == 0) break;
      }
    }
    return flow;
  }
  long long Maxflow(int s, int t) {
    this->s = s, this->t = t;
    long long flow = 0;
    while (BFS()) {
      memset(cur, 0, sizeof(cur));
      flow += DFS(s, INF);
    }
    return flow;
  }
} mf;
int n, m;
int U[M], V[M], W[M];
bool check(int x) {
  mf.init(2 * n + 5);
  int S = 0, T = 2 * n + 1;
  for (int i = 1; i <= n; ++i) mf.AddEdge(S, i, 1);
  for (int i = 1; i <= n; ++i) mf.AddEdge(n + i, T, 1);
  for (int i = 1; i <= m; ++i) {
    int u = U[i], v = V[i], w = W[i];
    if (w <= x) {
      mf.AddEdge(u, v + n, 1);
    }
  }
  return mf.Maxflow(S, T) == (long long)n;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int i = 1; i <= m; ++i) {
    cin >> U[i] >> V[i] >> W[i];
  }
  int l = 1, r = 1e9, ans = -1;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (check(mid))
      ans = mid, r = mid - 1;
    else
      l = mid + 1;
  }
  cout << ans << "\n";
  return 0;
}

```