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 <cstdlib>
#include <algorithm>
#include <cstring>
#include <queue>
#include <vector>
#include <functional>
#include <map>
#include <set>
#include <cmath>
#include <string>
#define SIZE 10005
#define INF 10000005

using namespace std;
typedef long long int ll;
typedef pair <int,int> P;

int V;
ll K;

struct edge{int to,cost;};
vector<edge> G[SIZE];
int d[SIZE];

void dijkstra(int s){
	priority_queue<P, vector<P>, greater<P>> que;
	fill(d,d+V,INF);
	d[s] = 0;
	que.push(P(0,s));

	while(!que.empty()){
		P p = que.top();que.pop();
		int v = p.second;
		if(d[v] < p.first)continue;
		for(int i=0;i<G[v].size();i++){
			edge e = G[v][i];
			if(d[e.to] > d[v] + e.cost){
				d[e.to] = d[v] + e.cost;
				que.push(P(d[e.to],e.to));
			}
		}
	}
}

int main()
{
	scanf("%d",&V);
	int u,k,v,c;
	for(int i=0;i<V;i++){
		scanf("%d%d",&u,&k);
		for(int j=0;j<k;j++){
			scanf("%d%d",&v,&c);
			G[u].push_back((edge){v,c});
		}
	}
	dijkstra(0);
	for(int i=0;i<V;i++){
		printf("%d %d\n",i,d[i]);
	}
	return 0;
}

