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 OCaml (4.10.0) (judge verdict: Wrong Answer)

let split_string ?(pattern="") = Str.split @@ Str.regexp pattern

let n = Scanf.sscanf (read_line ()) "%d" @@ fun n -> n
let a = read_line () |> split_string ~pattern:" " |> List.map int_of_string
let b = read_line () |> split_string ~pattern:" " |> List.map int_of_string

let () =
  let sum_a, sum_b = List.fold_left2 (fun (sum_a, sum_b) a b ->
      if a > b then (sum_a, sum_b + a - b)
      else (sum_a + (b - a) / 2, sum_b)
    ) (0, 0) a b in
  print_endline @@ if sum_a > sum_b then "Yes" else "No"