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
#include <cstdio>
#include <iostream>
#include <cmath>
#include <ctype.h>
#include <string>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <map>
#include <queue>
#include <utility>
#include <vector>
#include <set>
#include <list>
#include <cstring>
#include <stack>

using namespace std;

#define mod 1000000007

int main()
{
	int n;
	cin >> n;
	int ans[10001] = {};
	vector<vector<pair<int, int> > > graph(n + 1);
	for(int i = 0; i < n; i++){
		ans[i] = -1;
		int u, k;
		cin >> u >> k;
		for(int j = 0; j < k; j++){
			int v, c;
			cin >> v >> c;
			graph[u].push_back(make_pair(v, c));
		}
	}
	priority_queue<pair<int, int> > qu;
	qu.push(make_pair(0, 0));
	ans[0] = 0;
	while(!qu.empty()){
		int nowd = -(qu.top()).first;
		int nownode = (qu.top()).second;
		qu.pop();
		for(int i = 0; i < graph[nownode].size(); i++){
			int node = graph[nownode][i].first;
			int next = nowd + graph[nownode][i].second;
			if(ans[node] < 0 || ans[node] > next){
				ans[node] = next;
				qu.push(make_pair(-next, node));
			}
		}
	}
	for(int i = 0; i < n; i++){
		cout << i << " " << ans[i] << endl;
	}
}