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 (3.8.2) (judge verdict: Accepted)

def main():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    D = [a - b for a, b in zip(A, B)]
    # [0, 0, ..., 0]の数列に対し、「どれかを-2」「どれかを+1」をk回ずつやってDを作れるか？
    cnt_m2 = 0
    cnt_p1 = 0
    # 必要最低限な個数を計算
    for d in D:
        if d < 0:
            if d % 2 == 0:
                cnt_m2 += abs(d) // 2
            else:
                cnt_m2 += (abs(d) + 1) // 2
                cnt_p1 += 1
        elif d > 0:
            cnt_p1 += d
    # 基本的に「-2の回数」==「+1の回数」にできればYes。
    # ちなみに同じ数に対する操作として「-2の回数」:「+1の回数」=1:2 ならプラマイゼロで相殺されるので、
    # 相殺可能な操作を足して「-2の回数」==「+1の回数」にできればYes。
    # つまり cnt_m2 >= cnt_p1 ならYes。
    if cnt_m2 >= cnt_p1:
        print('Yes')
    else:
        print('No')


if __name__ == '__main__':
    main()