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There is a tree with vertices, numbered . For each , the -th edge connects Vertex and .

Taro has decided to paint each vertex in white or black. Here, it is not allowed to paint two adjacent vertices both in black.

Find the number of ways in which the vertices can be painted, modulo .

#### Constraints

- All values in input are integers.
- The given graph is a tree.

#### Input Specification

The first line will contain the integer .

The next lines will each contain 2 space separated integers .

#### Output Specification

Print the number of ways in which the vertices can be painted, modulo .

#### Sample Input 1

```
3
1 2
2 3
```

#### Sample Output 1

`5`

#### Explanation For Sample 1

There are five ways to paint the vertices, as follows:

#### Sample Input 2

```
4
1 2
1 3
1 4
```

#### Sample Output 2

`9`

#### Explanation For Sample 2

There are nine ways to paint the vertices, as follows:

#### Sample Input 3

`1`

#### Sample Output 3

`2`

#### Sample Input 4

```
10
8 5
10 8
6 5
1 5
4 8
2 10
3 6
9 2
1 7
```

#### Sample Output 4

`157`

## Comments

Can we assume the edge goes from to ? (As in, can we assume that the tree functions if you assume all the edges are directed?)

The graph is bidirectional.

Since it's a single tree, all the vertices will be part of the graph, right?

Yes.