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 heappush, heappop

def dijkstra(G, s):
    n = len(G)
    fixed = set()
    d = {}
    for i in range(n):
        d[i] = 9999999999999999999999999999999999999
    d[s] = 0
    heap = [(0, s)]
    while len(fixed) < n:
        du, u = heappop(heap)
        for v in G[u]:
            if v in fixed:
                continue
            if du + G[u][v] < d[v]:
                d[v] = du + G[u][v]
                heappush(heap, (d[v], v))
        fixed.add(u)
    return d




n = int(raw_input())
G = {}
for _ in range(n):
    entries = map(int, raw_input().split(' '))
    u = entries[0]
    k = entries[1]
    G[u] = {}
    for i in range(k):
        v = entries[i*2+2]
        c = entries[i*2+3]
        G[u][v] = c

d = dijkstra(G, 0)

for i in range(n):
    print i, d[i]