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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.chomp.to_i
a = gets.chomp.split(' ').map(&:to_i)
b = gets.chomp.split(' ').map(&:to_i)

c = []
n = 0
array_loop = true

N.times do |i|
  c.push a[i] - b[i]
end

loop do
  array_loop = false
  # +1 to b
  N.times do |k|
    if c[k] > 0
      c[k] -= 1
      break
    end
  end
  # +2 to a
  N.times do |j|
    if c[j] < 0
      c[j] += 2
      break
    end
  end
  # check all 0 in array (N > 1)
  (N - 1).times do |l|
    if c[l] != 0
      array_loop = true
    end
  end

  if (N == 1 && c[N - 1] > 0) || (N > 1 && array_loop && c[N - 1] > 0)
    puts 'No'
    break
  elsif (N == 1 && c[N - 1] == 0) || (N > 1 && array_loop && c[N - 1] == 0)
    puts 'Yes'
    break
  end
end