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

Solution (in JAVA):

Solution:
//package bubblecup13.f;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class B3 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";

	void solve()
	{
		int n = ni();
		int m = ni();
		int[] from = new int[m];
		int[] to = new int[m];
		int[] ws = new int[m];
		for(int i = 0;i < m;i++){
			from[i] = ni()-1;
			to[i] = ni()-1;
			ws[i] = ni();
		}

		int low = 0, high = 1000000007;
		while(high - low > 1){
			int h = high+low>>1;
			int[] lf = new int[m];
			int[] lt = new int[m];
			int p = 0;
			for(int i = 0;i < m;i++){
				if(ws[i] <= h){
					lf[p] = from[i];
					lt[p] = to[i];
					p++;
				}
			}
			if(p >= n && doBipartiteMatchingHK(packD(n, lf, lt, p), n) == n){
				high = h;
			}else{
				low = h;
			}
		}
		if(high > 1000000001){
			out.println(-1);
		}else {
			out.println(high);
		}
	}

	public static int[][] packD(int n, int[] from, int[] to) {
		return packD(n, from, to, from.length);
	}

	public static int[][] packD(int n, int[] from, int[] to, int sup) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int i = 0; i < sup; i++) p[from[i]]++;
		for (int i = 0; i < n; i++) g[i] = new int[p[i]];
		for (int i = 0; i < sup; i++) {
			g[from[i]][--p[from[i]]] = to[i];
		}
		return g;
	}


	public static int doBipartiteMatchingHK(int[][] g, int m)
	{
		int n = g.length;
		if(n == 0)return 0;
		int[] from = new int[m];
		int[] to = new int[n];
		Arrays.fill(to, -1);
		Arrays.fill(from, n);

		int[] d = new int[n+1];
		int mat = 0;
		while(true){
			Arrays.fill(d, -1);
			int[] q = new int[n];
			int r = 0;
			for(int i = 0;i < n;i++){
				if(to[i] == -1){
					d[i] = 0;
					q[r++] = i;
				}
			}

			for(int p = 0;p < r;p++) {
				int cur = q[p];
				for(int adj : g[cur]){
					int nex = from[adj];
					if(d[nex] == -1) {
						if(nex != n)q[r++] = nex;
						d[nex] = d[cur] + 1;
					}
				}
			}
			if(d[n] == -1)break;

			for(int i = 0;i < n;i++){
				if(to[i] == -1){
					if(dfsHK(d, g, n, m, to, from, i))mat++;
				}
			}
		}
		return mat;
	}

	static boolean dfsHK(int[] d, int[][] g, int n, int m, int[] to, int[] from, int cur)
	{
		if(cur == n)return true;
		for(int adj : g[cur]){
			int nex = from[adj];
			if(d[nex] == d[cur] + 1 && dfsHK(d, g, n, m, to, from, nex)){
				to[cur] = adj;
				from[adj] = cur;
				return true;
			}
		}
		d[cur] = -1;
		return false;
	}


	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new B3().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}