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
from heapq import heappop, heappush

def dijkstra(s):
    dp[s] = 0
    hq = []
    used[s] = 0
    for i in cost[s]:
        heappush(hq, i)

    while hq:
        minv = heappop(hq)
        if used[minv[1]] == 0:
            continue
        v = minv[1]
        dp[v] = minv[0]
        used[v] = 0
        for i in cost[v]:
            if used[i[1]]:
                heappush(hq, [i[0] + dp[v], i[1]])
    return

INF = 10 ** 18
n = int(input())
cost = [[] for _ in range(n)]
used = [1] * n
dp = [INF] * n

for i in range(n):
    lst = list(map(int, input().split()))
    for j in range(lst[1]):
        v, c = lst[2 + (2 * j)], lst[3 + (2 * j)]
        cost[lst[0]].append([c, v])

dijkstra(0)
for i in range(n):
    print(i, dp[i])
