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 <iostream>
#include <algorithm>
#include <cmath>

using namespace std;

typedef long long int ll;

ll x[1010];
ll y[1010];
ll dx[4] = {1, 0, -1, 0};
ll dy[4] = {0, 1, 0, -1};
char dir[4] = {'R', 'U', 'L', 'D'};

int main() {
    ll N;
    cin >> N;
    ll par = 0;
    for (ll i = 0; i < N; i++) {
        cin >> x[i] >> y[i];
        if (i == 0) par = x[i] + y[i];
        if ((par - (x[i] + y[i])) % 2 == 0) continue;
        cout << -1 << endl;
        return 0; 
    }
    if (par % 2 == 0) {
        cout << 32 << endl;
        cout << 1 << " ";
    } else {
        cout << 31 << endl;
    }
    for (ll i = 30; i >= 0; i--) {
        cout << ((ll)1 << i) << " ";
    }
    cout << endl;
    for (ll i = 0; i < N; i++) {
        if (par % 2 == 0) {
            x[i]--;
            cout << 'R';
        }
        for (ll stick = ((ll)1 << 30); stick >= 1; stick >>= 1) {
            for (ll j = 0; j < 4; j++) {
                ll tx = x[i] - stick * dx[j];
                ll ty = y[i] - stick * dy[j];
                if (abs(tx) + abs(ty) < stick) {
                    cout << dir[j];
                    x[i] = tx;
                    y[i] = ty;
                    break;
                }
            }
        }
        cout << endl;
    }
}