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
import heapq


def dijkstra(adj, s):
    INF = 200000
    n = len(adj)
    state, d, p = [False] * n, [INF] * n, [-1] * n
    d[s] = 0
    pq = [(d[s], s)]
    while pq:
        f, u = heapq.heappop(pq)
        state[u] = True
        if d[u] < f:
            continue
        for v, c in adj[u]:
            if state[v]:
                continue
            if d[u] + c < d[v]:
                d[v] = d[u] + c
                p[v] = u
                heapq.heappush(pq, (d[v], v))
    return d


def main():
    n = int(input())
    adj = [[] for _ in range(n)]
    for _ in range(n):
        u, _, *vc = map(int, input().split())
        for v, c in zip(vc[::2], vc[1::2]):
            adj[u].append((v, c))
    dist = dijkstra(adj, 0)
    for i, d in enumerate(dist):
        print(i, d)


if __name__ == '__main__':
    main()

