p03915 CODE FESTIVAL 2016 Final - Zigzag MST_9793
We have a graph with N vertices, numbered 0 through N-1. Edges are yet to be added.

We will process Q queries to add edges. In the i-th (1≦i≦Q) query, three integers A_i, B_i and C_i will be given, and we will add infinitely many edges to the graph as follows:

* The two vertices numbered A_i and B_i will be connected by an edge with a weight of C_i.
* The two vertices numbered B_i and A_i+1 will be connected by an edge with a weight of C_i+1.
* The two vertices numbered A_i+1 and B_i+1 will be connected by an edge with a weight of C_i+2.
* The two vertices numbered B_i+1 and A_i+2 will be connected by an edge with a weight of C_i+3.
* The two vertices numbered A_i+2 and B_i+2 will be connected by an edge with a weight of C_i+4.
* The two vertices numbered B_i+2 and A_i+3 will be connected by an edge with a weight of C_i+5.
* The two vertices numbered A_i+3 and B_i+3 will be connected by an edge with a weight of C_i+6.
* ...



Here, consider the indices of the vertices modulo N. For example, the vertice numbered N is the one numbered 0, and the vertice numbered 2N-1 is the one numbered N-1.

The figure below shows the first seven edges added when N=16, A_i=7, B_i=14, C_i=1:

<image>

After processing all the queries, find the total weight of the edges contained in a minimum spanning tree of the graph.

Constraints

* 2≦N≦200,000
* 1≦Q≦200,000
* 0≦A_i,B_i≦N-1
* 1≦C_i≦10^9

Input

The input is given from Standard Input in the following format:


N Q
A_1 B_1 C_1
A_2 B_2 C_2
:
A_Q B_Q C_Q


Output

Print the total weight of the edges contained in a minimum spanning tree of the graph.

Examples

Input

7 1
5 2 1


Output

21


Input

2 1
0 0 1000000000


Output

1000000001


Input

5 3
0 1 10
0 2 10
0 4 10


Output

42
import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int Q = sc.nextInt();
		int[] A = new int[Q];
		int[] B = new int[Q];
		long[] C = new long[Q];
		long[] min_cost = new long[N];
		Arrays.fill(min_cost, Long.MAX_VALUE/ 10);
		PriorityQueue<Edge> pq = new PriorityQueue<>();
		for (int i = 0; i < Q; ++i) {
			A[i] = sc.nextInt();
			B[i] = sc.nextInt();
			C[i] = sc.nextInt();
			pq.add(new Edge(A[i], B[i], C[i]));
			min_cost[A[i]] = Math.min(min_cost[A[i]], C[i] + 1);
			min_cost[B[i]] = Math.min(min_cost[B[i]], C[i] + 2);
		}
		for (int i = 0; i < 2 * N; ++i) {
			min_cost[(i + 1) % N] = Math.min(min_cost[(i + 1) % N], min_cost[i % N] + 2);
		}
		for (int i = 0; i < N; ++i) {
			pq.add(new Edge(i, (i + 1) % N, min_cost[i]));
		}
		DJSet ds = new DJSet(N);
		long ret = 0;
		while (!pq.isEmpty()) {
			Edge edge = pq.poll();
			if (ds.equiv(edge.a, edge.b))
				continue;
			ret += edge.cost;
			ds.setUnion(edge.a, edge.b);
			pq.add(new Edge(edge.b, (edge.a + 1) % N, edge.cost + 1));
		}
		System.out.println(ret);

	}

	static class DJSet {
		int n = 1;
		int[] upper;

		public DJSet(int n) {
			this.n = n;
			upper = new int[n];
			Arrays.fill(upper, -1);
		}

		int root(int x) {
			return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
		}

		boolean equiv(int x, int y) {
			return root(x) == root(y);
		}

		void setUnion(int x, int y) {
			x = root(x);
			y = root(y);
			if (x != y) {
				if (upper[x] < upper[y]) {
					int d = x;
					x = y;
					y = d;
				}
				upper[y] += upper[x];
				upper[x] = y;
			}
		}
	}

	static class Edge implements Comparable<Edge> {
		int a;
		int b;
		long cost;

		public Edge(int a, int b, long cost) {
			this.a = a;
			this.b = b;
			this.cost = cost;
		}

		@Override
		public int compareTo(Edge o) {
			return Long.compare(this.cost, o.cost);
		}
	}
}

7 1
5 2 1 2 1
0 0 1000000000 5 3
0 1 10
0 2 10
0 4 10 7 1
6 2 1 2 1
0 0 1000000010 5 3
0 0 10
0 2 10
0 4 10 9 1
6 2 1 5 3
0 0 10
0 3 10
0 4 10 9 1
7 2 1 9 1
5 2 1 7 1
5 4 1 2 1
0 0 0000000000 5 3
0 1 10
1 2 10
0 4 10 2 1
1 0 1000000010 9 1
6 2 0 2 1
0 0 0000000010 5 3
0 0 10
1 2 10
0 4 16 5 3
0 0 10
1 0 10
0 4 16 2 1
0 0 1000000100 5 3
0 1 10
0 2 7
0 4 10 2 1
0 0 1000001010 5 3
0 0 10
0 3 10
0 4 3 9 1
6 1 0 2 1
0 0 0000010010 9 1
1 2 0 12 1
3 2 1 2 1
0 0 1000010100 7 1
2 4 1 3 1
0 0 1000001010 2 1
0 0 0001010010 9 1
2 2 0 5 3
0 0 10
1 0 10
0 4 0 12 1
3 4 1 2 1
0 0 1000010110 3 1
1 0 1000001010 13 1
6 1 -1 5 3
0 0 10
0 2 10
1 4 2 12 1
3 4 2 2 1
0 0 1000010010 12 1
6 1 -1 21 1
3 4 2 12 1
2 1 -1 21 1
3 4 0 5 1
2 1 -1 21 1
3 4 1 5 1
1 1 -1 21 1
1 4 1 5 1
0 1 -1 21 1
0 4 1 9 1
0 1 -1 9 1
0 2 -1 6 1
5 2 1 2 1
0 0 1000100000 7 1
6 2 0 2 1
0 0 1000100010 9 1
6 4 1 5 3
0 1 10
1 2 10
0 4 9 4 1
1 0 1000000010 2 1
0 1 0000000010 12 1
5 2 0 7 1
2 0 1 2 1
0 0 1000001000 16 1
6 1 0 2 1
0 0 0000010011 4 1
0 0 1000001010 9 1
6 2 -1 12 1
6 4 1 4 1
1 0 1000001010 5 3
1 0 2
1 2 20
0 4 10 13 1
6 1 0 7 1
3 2 0 12 1
1 4 2 21 1
6 4 2 21 1
0 4 0 7 1
1 1 -1 21 1
1 0 1 2 1
1 1 -1 32 1
0 4 1 2 1
0 0 1000110010 9 1
6 4 2 3 1
1 0 1000000010 2 1
1 0 1000001000 5 3
0 0 10
0 0 10
1 4 3 8 3
0 0 10
1 2 10
0 4 10 5 3
1 0 14
1 2 10
0 4 21 12 1
0 2 0 9 1
6 6 1 5 3
1 0 1
1 2 20
0 4 10 13 1
6 1 1 12 1
1 7 2 21 1
6 4 1 21 1
1 4 0 32 1
0 5 1 3 1
2 0 1000000010 14 3
0 0 10
1 2 10
0 4 10 9 1
2 0 0 13 1
6 0 1 12 1
2 7 2 28 1
6 4 1 34 1
1 4 0 29 1
0 0 1 4 1
2 0 1000000010 2 1
1 1 0000011011
21 1000000001 42 22
 1000000011
 43
 36
 44
 37
 39
 31
 1
 42
 1000000010
 28
 11
 47
 49
 1000000101
 34
 1000001011
 21
 29
 10011
 56
 111
 1000010101
 27
 2000002024
 1010011
 64
 9
 121
 1000010111
 2000002021
 57
 14
 132
 1000010011
 45
 420
 89
 380
 5
 400
 12
 330
 8
 301
 48
 35
 15
 1000100001
 16
 1000100011
 46
 41
 3000000034
 10
 70
 24
 1000001001
 120
 10012
 3000003039
 20
 94
 3000003034
 17
 69
 25
 98
 366
 281
 30
 381
 0
 796
 1000110011
 54
 2000000021
 1000001000
 18
 85
 50
 91
 72
 13
 81
 77
 346
 310
 749
 2000000022
 223
 38
 78
 80
 654
 934
 812
 3000000033
 11012
