When Masha came to math classes today, she saw two integer sequences of length n - 1 on the blackboard. Let's denote the elements of the first sequence as a_i (0 ≤ a_i ≤ 3), and the elements of the second sequence as b_i (0 ≤ b_i ≤ 3).

Masha became interested if or not there is an integer sequence of length n, which elements we will denote as t_i (0 ≤ t_i ≤ 3), so that for every i (1 ≤ i ≤ n - 1) the following is true: 

  * a_i = t_i | t_{i + 1} (where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR)) and 
  * b_i = t_i \& t_{i + 1} (where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND)). 



The question appeared to be too difficult for Masha, so now she asked you to check whether such a sequence t_i of length n exists. If it exists, find such a sequence. If there are multiple such sequences, find any of them.

Input

The first line contains a single integer n (2 ≤ n ≤ 10^5) — the length of the sequence t_i. 

The second line contains n - 1 integers a_1, a_2, …, a_{n-1} (0 ≤ a_i ≤ 3) — the first sequence on the blackboard.

The third line contains n - 1 integers b_1, b_2, …, b_{n-1} (0 ≤ b_i ≤ 3) — the second sequence on the blackboard.

Output

In the first line print "YES" (without quotes), if there is a sequence t_i that satisfies the conditions from the statements, and "NO" (without quotes), if there is no such sequence.

If there is such a sequence, on the second line print n integers t_1, t_2, …, t_n (0 ≤ t_i ≤ 3) — the sequence that satisfies the statements conditions.

If there are multiple answers, print any of them.

Examples

Input

4
3 3 2
1 2 0


Output

YES
1 3 2 0 

Input

3
1 3
3 2


Output

NO

Note

In the first example it's easy to see that the sequence from output satisfies the given conditions: 

  * t_1 | t_2 = (01_2) | (11_2) = (11_2) = 3 = a_1 and t_1 \& t_2 = (01_2) \& (11_2) = (01_2) = 1 = b_1; 
  * t_2 | t_3 = (11_2) | (10_2) = (11_2) = 3 = a_2 and t_2 \& t_3 = (11_2) \& (10_2) = (10_2) = 2 = b_2; 
  * t_3 | t_4 = (10_2) | (00_2) = (10_2) = 2 = a_3 and t_3 \& t_4 = (10_2) \& (00_2) = (00_2) = 0 = b_3. 



In the second example there is no such sequence.
#include <bits/stdc++.h>
using namespace std;
int i, n, a[100000], b[100000], c[100000], k[2];
bool f(int i) {
  int j = 0, x = c[i];
  for (; j < 3 && !(((x | j) == a[i]) && ((x & j) == b[i])); j++)
    ;
  bool ans = ((x | j) == a[i] and (x & j) == b[i]);
  c[i + 1] = j;
  return ans;
}
int main() {
  string an[2] = {"NO", "YES"};
  int st = 0, j;
  for (cin >> n, i = 0; i < n - 1; cin >> a[i++])
    ;
  for (i = 0; i < n - 1; cin >> b[i++])
    ;
  for (k[0] = 0; k[0] < 4; k[0]++)
    for (k[1] = 0; k[1] < 4; k[1]++)
      if ((k[0] | k[1]) == a[0] and (k[0] & k[1]) == b[0])
        for (i = 0; i < 2 and !st; i++) {
          c[0] = k[i];
          c[1] = k[!i];
          for (j = 1; j < n - 2 and f(j); j++)
            ;
          if (n > 2)
            st = f(j);
          else
            st = 1;
        }
  cout << an[st] << endl;
  if (st)
    for (i = 0; i < n; i++) cout << c[i] << " ";
  return 0;
}
