Problem:
Score : 300 points

Problem Statement

You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N.
Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.

Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:

Add 2 to a_i.

Add 1 to b_j.

Constraints

1 ≤ N ≤ 10 000

0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N
b_1 b_2 .. b_N

Output

If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.

Sample Input 1

3
1 2 3
5 2 2

Sample Output 1

Yes

For example, we can perform three operations as follows to do our job:

First operation: i=1 and j=2. Now we have a = \{3,2,3\}, b = \{5,3,2\}.

Second operation: i=1 and j=2. Now we have a = \{5,2,3\}, b = \{5,4,2\}.

Third operation: i=2 and j=3. Now we have a = \{5,4,3\}, b = \{5,4,3\}.

Sample Input 2

5
3 1 4 1 5
2 7 1 8 2

Sample Output 2

No

Sample Input 3

5
2 7 1 8 2
3 1 4 1 5

Sample Output 3

No

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

import qualified Data.ByteString.Char8 as BC
import Data.Maybe (fromJust)
import Data.List
import Data.Array.IO

main = do
  n <- readLn :: IO Int
  a <- getIntListBC
  b <- getIntListBC
  let (x, y) = solve (zip a b) (0, 0)
      sa = sum a
      sb = sum b
      diff = sb - sa
  if (diff-x)*2 == (diff-y) && diff >= x && diff >= y
    then putStrLn "Yes"
    else putStrLn "No"

solve :: [(Int, Int)] -> (Int, Int) -> (Int, Int)
solve [] (x, y) = (x, y)
solve ((a,b):s) (x, y)
  | a < b = solve ((a+2, b):s) (x+1, y)
  | a > b = solve ((a, b+1):s) (x, y+1)
  | otherwise = solve s (x, y)

bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

getIntListBC :: IO [Int]
getIntListBC = map bsToInt . BC.words <$> BC.getLine