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: Wrong Answer)

N = int(input())
As = list(map(int, input().split()))
Bs = list(map(int, input().split()))

As.sort(reverse=True)
Bs.sort(reverse=True)

for iB in range(N):
    if As[iB] > Bs[iB]:
        d = As[iB] - Bs[iB]
        Bs[iB] += d
        rest = d * 2
        for iA in range(iB + 1, N):
            d = min(rest, max(0, (Bs[iA] - As[iA]) // 2 * 2))
            As[iA] += d
            rest -= d
            if rest == 0: break
        if rest > 0:
            print('No')
            exit()
    elif As[iB] < Bs[iB]:
        d = Bs[iB] - As[iB]
        As[iB] += d * 2
        Bs[iB] += d

print('Yes')