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_priorityqueue(s):
    global pq
    global d
    color=[0]*n
    d=[float('inf')]*n
    d[s]=0
    heapq.heappush(pq,[0,s])
    while len(pq)!=0:
        t,u=heapq.heappop(pq)
        color[u]=2
        if d[u]<t:
            continue
        j=-1
        for v in m[u][0::2]:
            j+=2
            if color[v]!= 2:
                if d[u]+m[u][j]<d[v]:
                    d[v]=d[u]+m[u][j]
                    color[v]=1
                    heapq.heappush(pq,[d[v],v])

n=input()
pq=[]
en=[]
m=[]
for i in xrange(n):
    en.append(map(int,raw_input().split()))
en.sort()
for i in xrange(n):
    m.append(en[i][2:])
dijkstra_priorityqueue(0)
for i in xrange(n):
    print i,d[i]