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 <cmath>

using namespace std;

typedef long long ll;

void solve(ll x, ll y, ll v[], int m) {
    int dx[4] = {-1, 0, 0, 1};
    int dy[4] = {0, -1, 1, 0};
    char mode[4] = {'R', 'U', 'D', 'L'};
    for (int i = 0; i < m; i++) {
        int dir = 0;
        ll t = abs(x + v[i] * dx[0]) + abs(y + v[i] * dy[0]);
        for (int j = 0; j < 4; j++) {
            ll nx = x + v[i] * dx[j];
            ll ny = y + v[i] * dy[j];
            if (abs(nx) + abs(ny) < t) {
                t = abs(nx) + abs(ny);
                dir = j;
            }
        }
        x = x + v[i] * dx[dir];
        y = y + v[i] * dy[dir];

        cout << mode[dir];
    }
    cout << endl;
    return;
}

int main() {
    int N, m = 34;
    ll X[1003], Y[1003];
    ll d[34];
    ll  t = 1;
    for (int i = 0; i < 33; i++) {
        d[32-i] = t;
        t *= 2;
    }
    d[33] = 1;

    cin >> N;

    int even = 0, odd = 0;

    for (int i = 0; i < N; i++) {
        cin >> X[i] >> Y[i];
        if ( ( abs(X[i]) + abs(Y[i])) % 2 == 0) {
            even++;
        } else {
            odd++;
        }
    }
    if (even && odd) {
        cout << -1 << endl;
        return 0;
    }

    if (odd) { m -= 1; }
    cout << m << endl;

    for (int i = 0; i < m; i++) {
        cout << d[i];
        if (i == m-1) { cout << endl; }
        else { cout << " "; }
    }
    for (int i = 0; i < N; i++) {
        solve(X[i], Y[i], d, m);
    }
    return 0;
}