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
# coding: utf-8
# Your code here!
import heapq

WHITE = 0
GRAY = 1
BLACK = 2

INF = 2000000000


def dijkstra():
    PQ = []
    heapq.heapify(PQ)
    color = [WHITE] * n
    d = [INF] * n
    
    d[0] = 0
    heapq.heappush(PQ, (0, 0))
    color[0] = GRAY
    
    while len(PQ) != 0:
        
        f = heapq.heappop(PQ)
        u = f[1]
        color[u] = BLACK
        
        if d[u] < f[0]:
            continue
        
        for j in range(len(adj[u])):
            v = adj[u][j][0]
            if color[v] == BLACK:
                continue
            if d[v] > d[u] + adj[u][j][1]:
                d[v] = d[u] + adj[u][j][1]
                heapq.heappush(PQ, (d[v], v))
                color[v] = GRAY
    for i in range(n):
        print(i, d[i])


n = int(input())

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

dijkstra()
        
        
        
        
        
        
        
        
        
        
        
        
