Problem:
Score : 100 points

Problem Statement

There is a tree with N vertices, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N - 1), the i-th edge connects Vertex x_i and y_i.

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 10^9 + 7.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq x_i, y_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_{N - 1} y_{N - 1}

Output

Print the number of ways in which the vertices can be painted, modulo 10^9 + 7.

Sample Input 1

3
1 2
2 3

Sample Output 1

5

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

Sample Input 2

4
1 2
1 3
1 4

Sample Output 2

9

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

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE BangPatterns      #-} --引数に!
{-# LANGUAGE MultiWayIf        #-}
{-# LANGUAGE TupleSections     #-}

import Data.List
import Data.Array.Unboxed
import Data.Array.MArray
import Data.Array.ST
import qualified Data.Vector.Unboxed as V (last,(!),fromList,Vector)
import Control.Monad
import Control.Monad.State
import Control.Monad.ST
import Debug.Trace

type Table = UArray (Int,Int) Bool -- True == White, x <= y
type DP s = STUArray s (Bool,Int) Int

dp_i :: DP s -> Table -> Int -> Int -> Int -> ST s () --(T+F or T)
dp_i dparr table n prev v = do
  let nh1 = map (\i -> if table!(v,i) then i else (-1)) (filter (/=prev) [v+1..n])
      nh2 = map (\i -> if table!(i,v) then i else (-1)) (filter (/=prev) [1..v-1])
      nh  = (filter (/=(-1)) nh1) ++ (filter (/=(-1)) nh2)
  if nh == []
      then forM_ [False,True] $ \c -> writeArray dparr (c,v) 1
      else do
        forM_ nh $ dp_i dparr table n v
        ls <- forM nh $ \v' -> do
          nextF <- readArray dparr (False,v')
          nextT <- readArray dparr (True,v')
          traceShowM ((v,v'),"nextT,nextF = ",nextT,nextF)
          return (nextT+nextF,nextT)
        writeArray dparr (False,v) $ mod0 $ foldl1' (*) (map snd ls)
        writeArray dparr (True,v)  $ mod0 $ foldl1' (*) (map fst ls)



solve :: [(Int,Int)] -> Int -> ST s Int
solve ls n = do
  table' <- newArray ((1,1),(n,n)) False :: ST s (STUArray s (Int,Int) Bool)
  forM_ ls $ \(x,y) -> writeArray table' (min x y,max x y) True
  table <- freeze table'
  dparr  <- newArray ((False,1),(True,n)) 0
  dp_i dparr table n (-1) 1
  ans0 <- forM [False,True] $ \c -> readArray dparr (c,1)
  return $ mod0 $ sum ans0


main :: IO ()
main = do
   n <- read <$> getLine
   ls <- replicateM (n-1) $ do
     (x:y:_) <- map read.words <$> getLine
     return (x,y)
   putStrLn $ show $ runST $ solve ls n

mod0 :: Int -> Int
mod0 n = mod n 1000000007