Forest

You are given a forest with N vertices and M edges. The vertices are numbered 0 through N-1. The edges are given in the format (x_i,y_i), which means that Vertex x_i and y_i are connected by an edge.

Each vertex i has a value a_i. You want to add edges in the given forest so that the forest becomes connected. To add an edge, you choose two different vertices i and j, then span an edge between i and j. This operation costs a_i + a_j dollars, and afterward neither Vertex i nor j can be selected again.

Find the minimum total cost required to make the forest connected, or print Impossible if it is impossible.

Constraints

• 1 ≤ N ≤ 100,000
• 0 ≤ M ≤ N-1
• 1 ≤ a_i ≤ 10^9
• 0 ≤ x_i,y_i ≤ N-1
• The given graph is a forest.
• All input values are integers.

Input

Input is given from Standard Input in the following format:

N M a_0 a_1 .. a_{N-1} x_1 y_1 x_2 y_2 : x_M y_M

Output

Print the minimum total cost required to make the forest connected, or print Impossible if it is impossible.

Examples

Input

7 5 1 2 3 4 5 6 7 3 0 4 0 1 2 1 3 5 6

Output

7

Input

5 0 3 1 4 1 5

Output

Impossible

Input

1 0 5

Output

0

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

N M a_0 a_1 .. a_{N-1} x_1 y_1 x_2 y_2 : x_M y_M

outputFormat

Output

Print the minimum total cost required to make the forest connected, or print Impossible if it is impossible.

Examples

Input

7 5 1 2 3 4 5 6 7 3 0 4 0 1 2 1 3 5 6

Output

7

Input

5 0 3 1 4 1 5

Output

Impossible

Input

1 0 5

Output

0

样例

1 0
5

0