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 <queue>	
#include <utility>	
#include <list>		
#define N 10000	
#define INF (1<<31-1);
using namespace std;

typedef pair<int,int> pii;	
vector<pii> adj[N];	
bool color[N];	
int dist[N];	
int n;	
priority_queue<pii> pq; 

int dijkstra(int k){	
	for(int i=0;i<n;i++){
		color[i]=false; 
		dist[i]=INF;	
	}
	color[k]=true; 
	dist[k]=0;	
	for(int i=0;i<adj[k].size();i++){
		pq.push(adj[k][i]); 
	}
	while(!pq.empty()){	
		pii temp=pq.top();pq.pop();	
		temp.first=-temp.first;	
		if(color[temp.second])continue;	
		color[temp.second]=true; 
		dist[temp.second]=temp.first;	
		for(int i=0;i<adj[temp.second].size();i++){
			if(!color[adj[temp.second][i].second])pq.push(make_pair(-dist[temp.second]+adj[temp.second][i].first,adj[temp.second][i].second));
		}
	}

	for(int i=0;i<n;i++) cout<<i<<" "<<dist[i]<<endl;
	return 0;
}
int main(void){
	int v,c;	
	int u,k;	
	cin>>n; 
	for(int i=0;i<n;i++){ 
		cin>>u>>k;	
		for(int j=0;j<k;j++){
			cin>>v>>c;	
			adj[u].push_back(make_pair(-c,v));	
		}
	}
	dijkstra(0);	
	return 0;
}