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.*;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

class Pair {
    int f, s;
    Pair(int f, int s) {
        this.f = f; this.s = s;
    }

    public boolean equals(Object o) {
        if(!(o instanceof Pair)) return false;
        Pair p = (Pair)o;
        return p.f==this.f && p.s==this.s;
    }
}
class PairComparator implements Comparator<Pair> {
    public int compare(Pair l, Pair r) {
        if (l.f != r.f) return l.f - r.f;
        else if(l.s != r.s)  return l.s - r.s;
        else return 0;
    }
}

public class Main {

    private static int[][] cost;
    private static int start_pos;
    private static int node_n;
    private static int[] d, prev;
    private static void dijkstra() {
        d = new int[node_n]; Arrays.fill(d, Integer.MAX_VALUE); d[start_pos] = 0;
        prev = new int[node_n];

        PriorityQueue<Pair> Q = new PriorityQueue<>(new PairComparator());
        for(int i=0; i<node_n; i++) Q.add(new Pair(d[i], i));

        while(!Q.isEmpty()) {
            Pair u = Q.poll();
            for(int v=0; v<node_n; v++) {
                if(cost[u.s][v] == Integer.MAX_VALUE) continue;
                int alt = d[u.s] + cost[u.s][v];
                if(d[v] > alt) {
                    d[v] = alt;
                    prev[v] = u.s;
                    Q.add(new Pair(d[v],v));
                }
            }
        }
    }

    public static void main(String[] args) throws IOException {

//        Scanner sc = new Scanner(System.in);
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());
        node_n = n; start_pos = 0;

        cost = new int[n][n];
        for(int[] c:cost) Arrays.fill(c, Integer.MAX_VALUE);
        for(int i=0; i<n; i++) {
            String[] in = br.readLine().split(" ", 0);
            int u = Integer.parseInt(in[0]), k = Integer.parseInt(in[1]);
            for(int j=0; j<k; j++) {
                int v = Integer.parseInt(in[2+2*j]), c = Integer.parseInt(in[2+2*j+1]);
                cost[u][v] = c;
            }
        }

        dijkstra();

        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        StringBuilder sb = new StringBuilder();
        for(int i=0; i<n; i++) {
            sb.append(i).append(" ").append(d[i]).append("\n");
        }
        bw.write(sb.toString());
        bw.flush();
    }
}
