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;
struct s {
  int ti, ti_1, ind;
};
int main() {
  int n;
  cin >> n;
  vector<int> a(n - 1);
  vector<int> b(n - 1);
  for (int i = 0; i < n - 1; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < n - 1; i++) {
    cin >> b[i];
  }
  vector<vector<s>> t(n - 1);
  for (int i = 0; i < n - 1; i++) {
    int a1 = a[i] >> 1, b1 = b[i] >> 1, a2 = a[i] & 1, b2 = b[i] & 1;
    if (a1 == 0 && b1 == 1 || a2 == 0 && b2 == 1) {
      cout << "NO";
      exit(0);
    }
    vector<s> cur;
    if (a1 == 0 && b1 == 0) {
      cur.push_back(s{0, 0, -1});
    } else if (a1 == 1 && b1 == 1) {
      cur.push_back(s{1, 1, -1});
    } else {
      cur.push_back(s{1, 0, -1});
      cur.push_back(s{0, 1, -1});
    }
    int cs = cur.size();
    for (int j = 0; j < cs; j++) {
      if (a2 == 0 && b2 == 0) {
        cur[j].ti = cur[j].ti << 1;
        cur[j].ti_1 = cur[j].ti_1 << 1;
      } else if (a2 == 1 && b2 == 1) {
        cur[j].ti = (cur[j].ti << 1) + 1;
        cur[j].ti_1 = (cur[j].ti_1 << 1) + 1;
      } else {
        int n = cur[j].ti, m = cur[j].ti_1;
        cur[j].ti = cur[j].ti << 1;
        cur[j].ti_1 = (cur[j].ti_1 << 1) + 1;
        cur.push_back(s{(n << 1) + 1, m << 1, -1});
      }
    }
    if (i == 0) {
      t[i] = cur;
    } else {
      for (int j = 0; j < t[i - 1].size(); j++) {
        for (int l = 0; l < cur.size(); l++) {
          if (t[i - 1][j].ti_1 == cur[l].ti) {
            cur[l].ind = j;
            t[i].push_back(cur[l]);
          }
        }
      }
    }
  }
  if (t[n - 2].size() == 0) {
    cout << "NO";
    exit(0);
  }
  vector<int> ans;
  ans.push_back(t[n - 2][0].ti_1);
  int ind = 0;
  for (int i = n - 2; i >= 0; i--) {
    ans.push_back(t[i][ind].ti);
    ind = t[i][ind].ind;
  }
  cout << "YES" << endl;
  for (int i = ans.size() - 1; i >= 0; i--) {
    cout << ans[i] << " ";
  }
}
