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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    private static ArrayList<ArrayList<Integer>> adjList;
    private static int[][] weights;
    private static int n;

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(in.readLine());
        adjList = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            adjList.add(new ArrayList<>());
        }
        weights = new int[n][n];
        for (int i = 0; i < n; i++) {
            String line = in.readLine();
            String[] data = line.split(" ");
            int u = Integer.parseInt(data[0]);
            int k = Integer.parseInt(data[1]);
            for (int j = 0; j < k*2; j+=2) {
                int v = Integer.parseInt(data[j+2]);
                int c = Integer.parseInt(data[j+3]);
                weights[u][v] = c;
                adjList.get(u).add(v);
            }
        }
        in.close();
        int[] dist = minDist();
        for (int i = 0; i < n; i++) {
            System.out.println(i + " " + dist[i]);
        }
    }

    private static int[] minDist() {
        int[] dist = new int[n];
        Arrays.fill(dist, Integer.MAX_VALUE);
        dist[0] = 0;
        PriorityQueue<Integer> fringe = new PriorityQueue<>(Comparator.comparingInt(x -> dist[x]));
        fringe.offer(0);
        while (!fringe.isEmpty()) {
            int u = fringe.poll();
            for (int v : adjList.get(u)) {
                int newDist = dist[u] + weights[u][v];
                if (newDist < dist[v]) {
                    fringe.remove(v);
                    dist[v] = newDist;
                    fringe.offer(v);
                }
            }
        }
        return dist;
    }
}


