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>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

int main(){
    int N;
    ll X[1000],Y[1000],U[1000],V[1000];
    
    cin >> N;
    for(int i=0;i<N;i++){
        cin >> X[i] >> Y[i];
        U[i]=X[i]+Y[i];
        V[i]=X[i]-Y[i];
    }
    for(int i=1;i<N;i++){
        if(((X[i]+Y[i])%2==0)!=((X[0]+Y[0])%2==0)){
            cout << -1 << endl;
            return 0;
        }
    }

    int m=31;
    if((X[0]+Y[0])%2==0) m++;
    cout << m << endl;
    cout << ((X[0]+Y[0])%2==0?"1 1":"1");
    for(int i=1;i<31;i++) cout << " " << (1LL<<i);
    cout << endl;
    for(int i=0;i<N;i++){
        string w="";
        if((X[0]+Y[0])%2==0){
            w="R";
            U[i]--;
            V[i]--;
        }
        ll u=((1LL<<31)-1-U[i])/2;
        ll v=((1LL<<31)-1-V[i])/2;
        for(int j=0;j<=30;j++){
            ll m=1LL<<j;
            if((u&m)==0 && (v&m)==0) w=w+"R";
            if((u&m)==0 && (v&m)!=0) w=w+"U";
            if((u&m)!=0 && (v&m)==0) w=w+"D";
            if((u&m)!=0 && (v&m)!=0) w=w+"L";
        }
        cout << w << endl;
    }
    
    return 0;
}