For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Constraints

* $1 \leq n \leq 10,000$
* $0 \leq c_i \leq 100,000$
* $|E| < 500,000$
* All vertices are reachable from vertex $0$

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Example

Input

5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3


Output

0 0
1 2
2 2
3 1
4 3

import java.io.File;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {

	static int n;
	@SuppressWarnings("unchecked")
	public static void main(String[] args) throws IOException {

		// input
		Scanner in = new Scanner(System.in);

		n = in.nextInt();
		List<List<Edge>> list = new ArrayList<>();
		Node[] nodeList = new Node[n];
		for (int i = 0; i < n; i++) {
			nodeList[i] = new Node(i, Integer.MAX_VALUE);
		}
		for (int i = 0; i < n; i++) {
			list.add(new ArrayList<Edge>());
		}
		for (int i = 0; i < n; i++) {
			int u = in.nextInt();
			int k = in.nextInt();
			for (int j = 0; j < k; j++) {
				int c = in.nextInt();
				int v = in.nextInt();
				list.get(u).add(new Edge(c, v));
			}
		}

		// solve
		PriorityQueue<Node> pq = new PriorityQueue<Node>(new MyComparator());
		boolean[] visited = new boolean[n];
		nodeList[0].cost = 0;
		pq.add(nodeList[0]);
		visited[0] = true;

		while (!pq.isEmpty()) {
			Node node = pq.poll();
			int fromNode = node.nodeNum;
			visited[node.nodeNum] = true;
			List<Edge> edges = list.get(fromNode);
			for (Edge edge : edges) {
				// 遷移先ノードのコストのほうが大きい場合は更新してキューに入れる
				if (nodeList[edge.toNodeNum].cost > nodeList[fromNode].cost + edge.weight) {
					nodeList[edge.toNodeNum].cost = nodeList[fromNode].cost + edge.weight;
					pq.add(nodeList[edge.toNodeNum]);
				}
			}
		}

		for (int i = 0; i < n; i++) {
			System.out.println(i + " " + nodeList[i].cost);
		}





	}

	@SuppressWarnings("rawtypes")
	static class MyComparator implements Comparator {

		public int compare(Object o1, Object o2) {

			Node n1 = (Node) o1;
			Node n2 = (Node) o2;

			int cost1 = n1.cost;
			int cost2 = n2.cost;

			if (cost1 > cost2) {
				return 1;
			} else if (cost1 < cost2) {
				return -1;
			} else {
				return 0;
			}
		}
	}

	static class Node {
		int nodeNum;
		int cost;

		public Node(int nodeNum, int weight) {
			this.nodeNum = nodeNum;
			this.cost = weight;
		}
	}
	static class Edge {
		int toNodeNum;
		int weight;

		public Edge(int nodeNum, int weight) {
			this.toNodeNum = nodeNum;
			this.weight = weight;
		}
	}

}

