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;

#define REP(i, n) for(int i = 0; i < n; i++)
#define REPR(i, n) for(int i = n; i >= 0; i--)
#define FOR(i, m, n) for(int i = m; i < n; i++)
#define ALL(obj) (obj).begin(), (obj).end()
#define INF 1e9
typedef long long ll;

typedef pair<ll,ll> P;

int main() {
    int N; cin >> N;
    vector<P> coord(N);
    REP(i,N){
        ll x,y; cin >> x >> y;
        coord[i] = {x,y};
    }
    int p = (abs(coord[0].first) + abs(coord[0].second))%2;
    REP(i,N){
        if(p != (abs(coord[i].first) + abs(coord[i].second))%2){
            cout << -1 << endl;
            return 0;
        }
    }

    vector<ll> D(39);
    REP(i,39){
        D[i] = (1LL<<(38-i));
    }
    if(p%2 == 0) D.push_back(1);

    cout << D.size() << endl;
    REP(i,D.size()){
        cout << D[i];
        if(i!=D.size()-1) cout << " ";
    }
    cout << endl;

    REP(i,N){
        ll X = coord[i].first, Y = coord[i].second;
        ll x=0, y=0;
        REP(i,D.size()){
            ll d = D[i];
            ll dx = X-x, dy = Y-y;

            if(abs(dx) > abs(dy)){
                if(dx>0){
                    cout << "R";
                    x += d;
                }else{
                    cout << "L";
                    x -= d;
                }
            }else{
                if(dy>0){
                    cout << "U";
                    y += d;
                }else{
                    cout << "D";
                    y -= d;
                }
            }
        }
        cout << endl;
        //cout << "(" << x << ", " << y << ")" << endl;
    } 

    return 0;
}