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())
numbersA = input().split()
numbersB = input().split()
sumA = 0
sumB = 0
diffNum = 0
diff = []
plusTotal = 0
minousTotal = 0
diffTotal = 0

for i in range(0,n):
	if numbersA[i] != numbersB[i]:
		diffNum += 1
	sumA += int(numbersA[i])
	sumB += int(numbersB[i])	
	diff.append((int(numbersB[i]) - int(numbersA[i])))
	if diff[i] < 0:
		minousTotal += 1
	elif diff[i] > 0:
		plusTotal += 1

# print(plusTotal)
if (sumA <= sumB) and (diffNum <= sumB - sumA) and minousTotal % 2 == 1 and plusTotal % 2 == 1:
	print("Yes")
else:
	print("No")

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