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())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
c = [a[i]-b[i] for i in range(n)]
d = sum(filter(lambda x:x<0, c))+2*sum(filter(lambda x:x>0, c))
if d > 0:
    print("No")
    exit()
elif d < 0:
    print("Yes")
    exit()
while sum(c) < 0:
    i,j,m = 0,0,0
    f_i,f_j = False,False
    for k in range(n):
        if c[k] == -1 and not f_i:
            i = k
            j = k
            f_i = True
            f_j = True
        if c[k] < -1 and not f_i:
            i = k
            f_i = True
        if c[k] > 0 and not f_j:
            j = k
            f_j = True
        if c[k] == 0:
            m = k
        if f_i and f_j:
            break
    if not f_j:
        j = m
    c[i] += 2
    c[j] -= 1
if len(list(filter(lambda x:x!=0, c))) > 0:
    print("No")
else:
    print("Yes")