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: Wrong Answer)

import Control.Applicative

main :: IO ()
main = do
    n <- readLn :: IO Int
    as <- (map read . words) <$> getLine
    bs <- (map read . words) <$> getLine
    let ds = zipWith (-) as bs
    print ds

    let res = foldl increment (0, 0) ds
    print res
    if fst res >= snd res then
        putStrLn "Yes"
    else
        putStrLn "No"
    where increment c d
            | d == 0 = c
            | d > 0 = incSnd c (abs d)
            | d < 0 = evenPattern c d
          evenPattern c d
            | d `mod` 2 == 0 = incFst c (abs $ d `div` 2)
            | otherwise = incSnd (incFst c ((abs $ (d - 1) `div` 2) )) 1


incFst :: (Int, Int) -> Int -> (Int, Int)
incFst c i = (fst c + i, snd c)

incSnd :: (Int, Int) -> Int -> (Int, Int)
incSnd c i = (fst c, snd c + i)