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F. The Shortest Statement

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a weighed undirected connected graph, consisting of $$$n$$$ vertices and $$$m$$$ edges.

You should answer $$$q$$$ queries, the $$$i$$$-th query is to find the shortest distance between vertices $$$u_i$$$ and $$$v_i$$$.

Input

The first line contains two integers $$$n$$$ and $$$m~(1 \le n, m \le 10^5, m - n \le 20)$$$ — the number of vertices and edges in the graph.

Next $$$m$$$ lines contain the edges: the $$$i$$$-th edge is a triple of integers $$$v_i, u_i, d_i~(1 \le u_i, v_i \le n, 1 \le d_i \le 10^9, u_i \neq v_i)$$$. This triple means that there is an edge between vertices $$$u_i$$$ and $$$v_i$$$ of weight $$$d_i$$$. It is guaranteed that graph contains no self-loops and multiple edges.

The next line contains a single integer $$$q~(1 \le q \le 10^5)$$$ — the number of queries.

Each of the next $$$q$$$ lines contains two integers $$$u_i$$$ and $$$v_i~(1 \le u_i, v_i \le n)$$$ — descriptions of the queries.

Pay attention to the restriction $$$m - n ~ \le ~ 20$$$.

Output

Print $$$q$$$ lines.

The $$$i$$$-th line should contain the answer to the $$$i$$$-th query — the shortest distance between vertices $$$u_i$$$ and $$$v_i$$$.

Examples

Input

3 3

1 2 3

2 3 1

3 1 5

3

1 2

1 3

2 3

Output

3

4

1

Input

8 13

1 2 4

2 3 6

3 4 1

4 5 12

5 6 3

6 7 8

7 8 7

1 4 1

1 8 3

2 6 9

2 7 1

4 6 3

6 8 2

8

1 5

1 7

2 3

2 8

3 7

3 4

6 8

7 8

Output

7

5

6

7

7

1

2

7

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