Problem Statement

Given is a simple undirected graph with N vertices and M edges. The vertices are numbered $1, \cdots, N$, and the i-th edge connects Vertices a_i and b_i.
Also given is a sequence of positive integers: $c_1, c_2, \cdots, c_N$.
Convert this graph into a directed graph that satisfies the condition below, that is, for each i, delete the undirected edge (a_i, b_i) and add one of the two direted edges $a_i \to$ b_i and $b_i \to$ a_i.

• For every $i = 1, 2, \cdots, N,$ there are exactly c_i vertices reachable from Vertex i (by traversing some number of directed edges), including Vertex i itself.

In this problem, it is guaranteed that the given input always has a solution.

Input

Input is given from Standard Input in the following format:
N M
a_1 b_1
:
a_M b_M
c_1 c_2 ... c_N

Output

Print M lines.
To add the edge $a_i \to$ b_i for the i-th edge, print -> in the i-th line; to add the edge $b_i \to$ a_i for the i-th edge, print <-.
If there are multiple solutions, any of them will be accepted.

Constraints

• $1 \leq N \leq 100$
• $0 \leq M \leq \frac{N(N - 1)}{2}$
• $1 \leq a_i, b_i \leq N$
• The given graph has no self-loops and no multi-edges.
• $1 \leq c_i \leq N$
• There always exists a valid solution.

Sample Input 1

3 3
1 2
2 3
3 1
3 3 3

Sample Output 1

->
->
->

In a cycle of length 3, you can reach every vertex from any vertex.

Sample Input 2

3 2
1 2
2 3
1 2 3

Sample Output 2

<-
<-

Sample Input 3

6 3
1 2
4 3
5 6
1 2 1 2 2 1

Sample Output 3

<-
->
->

The graph may be disconnected.

见题面 Input 部分

见题面 Output 部分