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 <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
const int maxx=10010;
const int infinity=1<<30;

int main() {
	int n,a,b,c,e;
	vector<pair<int, int> > A[maxx];
	bool flag[maxx];
	int d[maxx];
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a>>b;
		for(int j=0;j<b;j++){
			cin>>c>>e;
			A[a].push_back(make_pair(c,e));
		}
	}
	for(int i=0;i<n;i++){
		flag[i]=false;
		d[i]=infinity;
	}
	priority_queue<pair<int,int> > PQ;
	d[0]=0;
	PQ.push(make_pair(0, 0));
	while(PQ.empty()==0){
		pair<int, int> u=PQ.top();
		PQ.pop();
		//cout<<u.first<<" "<<d[u.first]<<endl;
		flag[u.second]=true;
		int len=A[u.second].size();
		for(int i=0;i<len;i++){
			int v=A[u.second][i].first;
			if(flag[v]==false && d[u.second]+A[u.second][i].second<d[v]){
				d[v]=d[u.second]+A[u.second][i].second;
				PQ.push(make_pair(d[v]*(-1),v));
			}
		}
	}

	for(int i=0;i<n;i++) cout<<i<<" "<<(d[i]==infinity ? -1 : d[i])<<endl;

	return 0;
}
