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 sys import stdin
input = stdin.readline
import heapq

infty = 2**21

def dijkstra(n):
    d = [infty] * n
    color = [0] * n

    d[0] = 0
    PQ = [(0, 0)]
    heapq.heapify(PQ)
    color[0] = 1

    while PQ:
        f = heapq.heappop(PQ)
        u = f[1]
        color[u] = 2

        #最小値を取り出し、それが最短でなければ無視
        if d[u] < f[0]:
            continue

        for adj_u in adj[u]:
            v = adj_u[0]
            if color[v] == 2:
                continue
            if d[v] > d[u] + adj_u[1]:
                d[v] = d[u] + adj_u[1]
                heapq.heappush(PQ, (d[v], v))
                color[v] = 1


    for i in range(n):
        print(str(i) + ' ' + str(-1 if d[i] == infty else d[i]))


n = int(input())

adj = [0]*n

for _ in range(n):
    u, k, *vc = map(int, input().split())
    vx_tuple = [0] * k
    for i, (v, c) in enumerate(zip(vc[::2], vc[1::2])):
        #pythonにはvectorないので、tupleで代用
        vx_tuple[i] = (v, c)
    adj[u] = vx_tuple


dijkstra(n)

