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 <queue>
#include <vector>
using namespace std;
#define INF 1 << 30
typedef pair<int, int> P;

int n, d[10000];
vector<P> M[10000];

void dijkstra(void) {
    int i, u, v;
    P t;
    priority_queue<P, vector<P>, greater<P> > pq;

    pq.push(make_pair(0, 0));
    while (!pq.empty()) {
        t = pq.top(); pq.pop();
        v = t.first;
        u = t.second;

        if (d[u] != INF) continue;
        d[u] = v;

        for (i = 0; i < M[u].size(); i++) {
            t = M[u][i];
            if (d[t.second] != INF) continue;
            pq.push(make_pair(v + t.first, t.second));
        }
    }
}

int main(void) {
    int i, j, u, k, v, c;
    scanf("%d", &n);

    for (i = 0; i < n; i++) d[i] = INF;

    for (i = 0; i < n; i++) {
        scanf("%d %d", &u, &k);
        for (j = 0; j < k; j++) {
            scanf("%d %d", &v, &c);
            M[u].push_back(make_pair(c, v));
        }
    }

    dijkstra();

    for (i = 0; i < n; i++) printf("%d %d\n", i, d[i]);

    return 0;
}