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 Python (3.4.3) (judge verdict: Runtime Error)

if __name__ == "__main__":
    N = int(input())
    A = list(map(int, (input().split(' '))))
    B = list(map(int, (input().split(' '))))

    move = sum(B) - sum(A)
    # A行目が大きい場合は、B行目は+１ずつしかできないので追い越せない。
    if move < 0:
        print('No')
        return 0
    Amove = 0
    Bmove = 0
    # 3 4 2
    # 5 3 4
    for i in range(N):
        # A[i] = 4, B[i] = 3 -> Amove = 1
        if A[i] > B[i]:
            Amove += A[i] - B[i]
        # A[i] = 3, B[i] = 5 -> Bmove = 1
        # A[i] = 2, B[i] = 4 -> Bmove = 1
        elif A[i] < B[i]:
            Bmove += (B[i] - A[i]) // 2
    # Amove = 1, Bmove = 1
    if Amove > Bmove:
        print('No')
    else:
        print('Yes')