Problem: Snuke is introducing a robot arm with the following properties to his factory:

* The robot arm consists of m sections and m+1 joints. The sections are numbered 1, 2, ..., m, and the joints are numbered 0, 1, ..., m. Section i connects Joint i-1 and Joint i. The length of Section i is d_i.
* For each section, its mode can be specified individually. There are four modes: `L`, `R`, `D` and `U`. The mode of a section decides the direction of that section. If we consider the factory as a coordinate plane, the position of Joint i will be determined as follows (we denote its coordinates as (x_i, y_i)):
* (x_0, y_0) = (0, 0).
* If the mode of Section i is `L`, (x_{i}, y_{i}) = (x_{i-1} - d_{i}, y_{i-1}).
* If the mode of Section i is `R`, (x_{i}, y_{i}) = (x_{i-1} + d_{i}, y_{i-1}).
* If the mode of Section i is `D`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} - d_{i}).
* If the mode of Section i is `U`, (x_{i}, y_{i}) = (x_{i-1}, y_{i-1} + d_{i}).



Snuke would like to introduce a robot arm so that the position of Joint m can be matched with all of the N points (X_1, Y_1), (X_2, Y_2), ..., (X_N, Y_N) by properly specifying the modes of the sections. Is this possible? If so, find such a robot arm and how to bring Joint m to each point (X_j, Y_j).

Constraints

* All values in input are integers.
* 1 \leq N \leq 1000
* -10^9 \leq X_i \leq 10^9
* -10^9 \leq Y_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
X_1 Y_1
X_2 Y_2
:
X_N Y_N


Output

If the condition can be satisfied, follow the following format. If the condition cannot be satisfied, print `-1`.


m
d_1 d_2 ... d_m
w_1
w_2
:
w_N


m and d_i are the configurations of the robot arm. Refer to the problem statement for what each of them means. Here, 1 \leq m \leq 40 and 1 \leq d_i \leq 10^{12} must hold. Also, m and d_i must all be integers.

w_j is a string of length m that represents the way to bring Joint m of the robot arm to point (X_j, Y_j). The i-th character of w_j should be one of the letters `L`, `R`, `D` and `U`, representing the mode of Section i.

Examples

Input

3
-1 0
0 3
2 -1


Output

2
1 2
RL
UU
DR


Input

5
0 0
1 0
2 0
3 0
4 0


Output

-1


Input

2
1 1
1 1


Output

2
1 1
RU
UR


Input

3
-7 -3
7 3
-3 -7


Output

5
3 1 4 1 5
LRDUL
RDULR
DULRD

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#include <unordered_map>
#include <queue>
#define MOD 1000000007
using namespace std;

int main() {
    int N,i,j,cnt=0;
    long long X[1000], Y[1000];
    cin>>N;
    for(i=0;i<N;i++){
        cin>>X[i]>>Y[i];
        if(abs(X[0]+Y[0])%2!=abs(X[i]+Y[i])%2){
            cout<<-1;
            return 0;
        }
    }
    long long d[40];
    for(i=32;i>=0;--i){
        d[cnt++]=(1ll<<i);
    }
    if((X[0]+Y[0])%2==0)d[cnt++]=1;

    cout<<cnt<<endl;
    for(i=0;i<cnt;i++){
        cout<<d[i]<<" ";
    }
    cout<<endl;

    for(i=0;i<N;i++){
        string s;
        for(j=0;j<cnt;j++){
            if(abs(X[i])>=abs(Y[i])){
                if(X[i]<=0){
                    X[i]+=d[j];
                    s+='L';
                }else{
                    X[i]-=d[j];
                    s+='R';
                }
            }else{
                if(Y[i]<=0){
                    Y[i]+=d[j];
                    s+='D';
                }else{
                    Y[i]-=d[j];
                    s+='U';
                }
            }
        }
        cout<<s<<endl;
    }
    return 0;
}