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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

var
 n,i,j,t:longint;
 a,b:array[0..10001] of longint;
 p:boolean;
begin
 readln(n);
 for i:=1 to n do
  read(a[i]);
 readln;
 for i:=1 to n do 
  read(b[i]);
 for i:=1 to n-1 do
  for j:=i+1 to n do 
   if a[i]<a[j] then
    begin
     t:=a[i]; a[i]:=a[j]; a[j]:=t;
    end; 
 for i:=1 to n-1 do
  for j:=i+1 to n do 
   if b[i]<b[j] then
    begin
     t:=b[i]; b[i]:=b[j]; b[j]:=t;
    end; 
 for i:=1 to n do 
  if b[i]<a[i] then
   begin
    p:=true;
    break;
   end;
 if p then writeln('No')
  else writeln('Yes');
end.