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>
#define int long long

using namespace std;


/*
void(build(int a[],int v,int tl,int tr)){
    if(tl==tr){
        t[v]=a[tl];
    }
    else{
        int tm=(tr+tl)/2;
        build(a,v*2,tl,tm);
        build(a,v*2+1,tm+1,tr);
        t[v]=t[v*2]+t[v*2+1];
    }
}

void update(int v,int tl,int tr,int pos,int val){
    if(tl==tr){
        t[v]=val;
    }
    else{
        int tm=(tl+tr)/2;
        if(pos<=tm){
            update(v*2,tl,tm,pos,val);
        }
        else{
            update(v*2+1,tm+1,tr,pos,val);
        }
        t[v]=t[v*2]+t[v*2+1];
    }
}

int sum(int v,int tl,int tr,int l,int r){
    if(l>r){
        return 0;
    }
    if(l==tl&&r==tr){
        return t[v];
    }
    int tm=(tl+tr)/2;
    return sum(v*2,tl,tm,l,min(tm,r))+sum(v*2+1,tm+1,tr,max(tm+1,l),r);
}
*/


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];
    }
    int boo=0;
    vector<int> t(n,-1);
    for(int j=0;j<=3;j++){
        t[0]=j;
        for(int i=0;i<n-1;i++){
            if(a[i]==3&&b[i]==3&&t[i]==3){
                t[i+1]=3;
            }
            else if(a[i]==2&&b[i]==2&&t[i]==2){
                t[i+1]=2;
            }
            else if(a[i]==3&&b[i]==2&&t[i]==2){
                t[i+1]=3;
            }
            else if(a[i]==3&&b[i]==2&&t[i]==3){
                t[i+1]=2;
            }
            else if(a[i]==1&&b[i]==1&&t[i]==1){
                t[i+1]=1;
            }
            else if(a[i]==3&&b[i]==1&&t[i]==3){
                t[i+1]=1;
            }
            else if(a[i]==3&&b[i]==1&&t[i]==1){
                t[i+1]=3;
            }
            else if(a[i]==0&&b[i]==0&&t[i]==0){
                t[i+1]=0;
            }
            else if(a[i]==1&&b[i]==0&&t[i]==0){
                t[i+1]=1;
            }
            else if(a[i]==1&&b[i]==0&&t[i]==1){
                t[i+1]=0;
            }
            else if(a[i]==2&&b[i]==0&&t[i]==2){
                t[i+1]=0;
            }
            else if(a[i]==2&&b[i]==0&&t[i]==0){
                t[i+1]=2;
            }
            else if(a[i]==3&&b[i]==0&&t[i]==0){
                t[i+1]=3;
            }
            else if(a[i]==3&&b[i]==0&&t[i]==3){
                t[i+1]=0;
            }
            else{
                boo++;
                break;
            }
        }
        if(boo==0){
            cout<<"YES"<<endl;
            for(int i=0;i<n;i++){
                cout<<t[i]<<' ';
            }
            return 0;
        }
        else{
            boo=0;
        }
    }


    cout<<"NO";
    return 0;
}