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.
var n = +readline();
var a = readline().split(' ').map(v=>+v);
var b = readline().split(' ').map(v=>+v);

var map = {};
for(var i = 0; i < 4; i++) {
    for(var j = i; j < 4; j++) {
        var aValue = i | j;
        var bValue = i & j;
        var ind = aValue * 10 + bValue;
        if(!map[ind]) map[ind] = [];           
        map[ind].push([i, j]);
    }
}

var t;
var check = function(i) {
   if(i === a.length) return true;
   var couplesArr = map[a[i] * 10 + b[i]];
   if(!couplesArr) return false;
   
   var res = false;
   for(var j = 0; j < couplesArr.length; j++) {
      var couple = couplesArr[j];
      if(!i) {
         t = [couple[0], couple[1]];
         res = check(i + 1);
      } else if(couple[0] !== t[i] && couple[1] !== t[i]){
         res = false;   
      } else {
         t[i+1] = couple[0] !== t[i] ? couple[0] : couple[1];
         res = check(i + 1);
      } 
      if(res) break;
   }
   
   return res; 
}

var final = check(0);

print(final ? 'YES' : 'NO');
if(final) {
    print(t.join(' '));    
}