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: Time Limit Exceeded)

n = gets.to_i
a = gets.split.map{|s|s.to_i}.sort
b = gets.split.map{|s|s.to_i}.sort

try =  b.inject{|s,i|s+i} - a.inject{|s,i|s+i}
if try < 0
  puts "No"
elsif try == 0 && a == b
  puts "Yes"
else
  try.times do
    a.size.times do |i|
      if a[i] == b[i]
        next
      elsif a[i] + 2 ==  b[i]
        a[i] += 2
        b[i+1] or b[i] += 1
      else a[i] + 2 == b[i] + 1
        a[i] += 2
        b[i] += 1
      end
    end
  end
  puts (a == b) ? 'Yes' : 'No'
end