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;

pair<int, int> pos[200005];
pair<int, int> poss[200005];

int main()
{
    int n;
    cin >> n;
    for(int i = 0; i < n; ++i){
        cin >> pos[i].first >> pos[i].second;
        poss[i] = {pos[i].first + pos[i].second, pos[i].first - pos[i].second};
    }

    int par = abs(pos[0].first + pos[0].second) % 2;
    for(int i = 1; i < n; ++i){
        if(abs(pos[i].first + pos[i].second) % 2 != par){
            cout << "-1\n";
            return 0;
        }
    }

    vector<int> d;
    for(int i = 30; i >= 0; --i){
        d.push_back((1LL << i));
    }
    if(!par){
        d.push_back(1);
    }

    cout << (int)d.size() << "\n";
    for(auto x : d){
        cout << x << " ";
    }
    cout << "\n";

    for(int i = 0; i < n; ++i){
        int xdir, ydir;
        int xcur = 0, ycur = 0;
        for(int j = 0; j < (int)d.size(); ++j){
            if(xcur > poss[i].first){
                xdir = -1;
                xcur -= d[j];
            }else{
                xdir = 1;
                xcur += d[j];
            }
            if(ycur > poss[i].second){
                ydir = -1;
                ycur -= d[j];
            }else{
                ydir = 1;
                ycur += d[j];
            }

            if(xdir == 1 && ydir == 1)cout << "R";
            else if(xdir == 1 && ydir == -1)cout << "U";
            else if(xdir == -1 && ydir == -1)cout << "L";
            else cout << "D";
        }
        cout << "\n";
    }
    return 0;
}