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 <vector>
#include <queue>
#include <utility>
using namespace std;
typedef pair<int,int> pp;
const int INF = 1001001001;
struct edge{int to, cost;};

int main() {
    int V;
    cin >> V;
    vector< vector<edge> > A(V);
    for(int i=0; i<V; i++) {
        int u,k;
        cin >> u >> k;
        A[u].resize(k);
        for(int j=0; j<k; j++) {
            int v,c;
            cin >> v >> c;
            struct edge e = {v,c};
            A[u][j] = e;
        }
    }

    vector<int> d(V,INF);
    d[0] = 0;
    priority_queue< pp, vector<pp>, greater<pp> > Q;
    Q.push(pp(d[0],0));
    
    while(!(Q.empty())) {
        pp temp = Q.top();
        Q.pop();
        int ct = temp.first;
        int u = temp.second;
        for(int j=0; j<A[u].size(); j++) {
            int v = A[u][j].to;
            int tmpcost = A[u][j].cost;
            if(d[v] > ct + tmpcost) {
                d[v] = ct + tmpcost;
                Q.push(pp(d[v], v));
            }
        }
    }

    for(int i=0; i<V; i++) cout << i << " " << d[i] << endl;
    return 0;
}
