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:
//By Bibi
///                 .-~~~~~~~~~-._       _.-~~~~~~~~~-.
///             __.'              ~.   .~              `.__
///           .'//                  \./                  \`.
///        .'//                     |                     \`.
///       .'// .-~"""""""~~~~-._     |     _,-~~~~"""""""~-. \`.
///     .'//.-"                 `-.  |  .-'                 "-.\`.
///   .'//______.============-..   \ | /   ..-============.______\`.
/// .'______________________________\|/______________________________`.
#include <bits/stdc++.h>
using namespace std;
 
const int N = 1010;
int n, X[N], Y[N];
char s[40];
 
int iabs(int x) { return x > 0 ? x : -x; }
 
int main() {
    scanf("%d", &n);
    int c = 0;
    for (int i = 1; i <= n; i++) {
        scanf("%d%d", &X[i], &Y[i]);
        if ((X[i] + Y[i]) & 1) c++;
        else c--;
    }
    if (iabs(c) != n) {
        puts("-1"); return 0;
    }
    int m = 31 + (c < 0);
    printf("%d\n", m);
    for (int i = 0; i <= 30; i++) printf("%d ", 1 << i);
    if (c < 0) printf("1 ");
    puts("");
    for (int i = 1; i <= n; i++) {
        int x = X[i], y = Y[i], sign = 0;
        if (c < 0) s[31] = 'R', x--;
        for (int j = 30; j >= 0; j--) {
            if (iabs(x) < iabs(y)) swap(x, y), sign ^= 1;
            if (x > 0) x -= 1 << j, s[j] = sign ? 'U' : 'R';
            else x += 1 << j, s[j] = sign ? 'D' : 'L';
        }
        printf("%s\n", s);
    }
    return 0;
}