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.
n = int(input())
a = [int(i) for i in input().split()]
b = [int(i) for i in input().split()]
matr = [[(), (), (), ()], [(), (), (), ()], [(), (), (), ()], [(), (), (), ()]]
matr[0][0] = (0, 0)
matr[0][1] = (-1, -1)
matr[0][2] = (-1, -1)
matr[0][3] = (-1, -1)
matr[1][0] = (1, 0)
matr[1][1] = (1, 1)
matr[1][2] = (-1, -1)
matr[1][3] = (-1, -1)
matr[2][0] = (2, 0)
matr[2][1] = (-1, -1)
matr[2][2] = (2, 2)
matr[2][3] = (-1, -1)
matr[3][1] = (1, 3)
matr[3][2] = (3, 2)
matr[3][3] = (3, 3)
t = []
if (a[0] != 3 or b[0] != 0) and matr[a[0]][b[0]][0] == -1:
    print('NO')
    exit(0)
else:
    if a[0] == 3 and b[0] == 0:
        t.append(3)
        t.append(0)
        f = False
        for i in range(1, n - 1):
            if a[i] == 3 and b[i] == 0:
                if t[i] == 0:
                    t.append(3)
                elif t[i] == 1:
                    t.append(2)
                elif t[i] == 2:
                    t.append(1)
                else:
                    t.append(0)
            elif matr[a[i]][b[i]][0] != t[i] and matr[a[i]][b[i]][1] != t[i]:
                f = True
                break
            else:
                if matr[a[i]][b[i]][0] == t[i]:
                    t.append(matr[a[i]][b[i]][1])
                else:
                    t.append(matr[a[i]][b[i]][0])
        if not f:
            print('YES')
            print(*t)
        else:
            t = []
            t.append(0)
            t.append(3)
            f = False
            for i in range(1, n - 1):
                if a[i] == 3 and b[i] == 0:
                    if t[i] == 0:
                        t.append(3)
                    elif t[i] == 1:
                        t.append(2)
                    elif t[i] == 2:
                        t.append(1)
                    else:
                        t.append(0)
                elif matr[a[i]][b[i]][0] != t[i] and matr[a[i]][b[i]][1] != t[i]:
                    f = True
                    break
                else:
                    if matr[a[i]][b[i]][0] == t[i]:
                        t.append(matr[a[i]][b[i]][1])
                    else:
                        t.append(matr[a[i]][b[i]][0])
            if not f:
                print('YES')
                print(*t)
            else:
                t = []
                t.append(1)
                t.append(2)
                f = False
                for i in range(1, n - 1):
                    if a[i] == 3 and b[i] == 0:
                        if t[i] == 0:
                            t.append(3)
                        elif t[i] == 1:
                            t.append(2)
                        elif t[i] == 2:
                            t.append(1)
                        else:
                            t.append(0)
                    elif matr[a[i]][b[i]][0] != t[i] and matr[a[i]][b[i]][1] != t[i]:
                        f = True
                        break
                    else:
                        if matr[a[i]][b[i]][0] == t[i]:
                            t.append(matr[a[i]][b[i]][1])
                        else:
                            t.append(matr[a[i]][b[i]][0])
                if not f:
                    print('YES')
                    print(*t)
                else:
                    t = []
                    t.append(2)
                    t.append(1)
                    f = False
                    for i in range(1, n - 1):
                        if a[i] == 3 and b[i] == 0:
                            if t[i] == 0:
                                t.append(3)
                            elif t[i] == 1:
                                t.append(2)
                            elif t[i] == 2:
                                t.append(1)
                            else:
                                t.append(0)
                        elif matr[a[i]][b[i]][0] != t[i] and matr[a[i]][b[i]][1] != t[i]:
                            f = True
                            break
                        else:
                            if matr[a[i]][b[i]][0] == t[i]:
                                t.append(matr[a[i]][b[i]][1])
                            else:
                                t.append(matr[a[i]][b[i]][0])
                    if not f:
                        print('YES')
                        print(*t)
                    else:
                        print('NO')
    else:
        t.append(matr[a[0]][b[0]][0])
        t.append(matr[a[0]][b[0]][1])
        f = False
        for i in range(1, n - 1):
            if a[i] == 3 and b[i] == 0:
                if t[i] == 0:
                    t.append(3)
                elif t[i] == 1:
                    t.append(2)
                elif t[i] == 2:
                    t.append(1)
                else:
                    t.append(0)
            elif matr[a[i]][b[i]][0] != t[i] and matr[a[i]][b[i]][1] != t[i]:
                f = True
                break
            else:
                if matr[a[i]][b[i]][0] == t[i]:
                    t.append(matr[a[i]][b[i]][1])
                else:
                    t.append(matr[a[i]][b[i]][0])
        if not f:
            print('YES')
            print(*t)
        else:
            t = []
            t.append(matr[a[0]][b[0]][1])
            t.append(matr[a[0]][b[0]][0])
            f = False
            for i in range(1, n - 1):
                if a[i] == 3 and b[i] == 0:
                    if t[i] == 0:
                        t.append(3)
                    elif t[i] == 1:
                        t.append(2)
                    elif t[i] == 2:
                        t.append(1)
                    else:
                        t.append(0)
                elif matr[a[i]][b[i]][0] != t[i] and matr[a[i]][b[i]][1] != t[i]:
                    f = True
                    break
                else:
                    if matr[a[i]][b[i]][0] == t[i]:
                        t.append(matr[a[i]][b[i]][1])
                    else:
                        t.append(matr[a[i]][b[i]][0])
            if not f:
                print('YES')
                print(*t)
            else:
                print('NO')
