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 <algorithm>
#include <cstdio>
#include <cstring>

#define int long long
#define Accepted 0; 

const int Maxv = 100010; 

int dis[Maxv], x[Maxv], y[Maxv], n, m = 40; 
bool flag1, flag2; 

inline void LiXinLongWalking(int x, int y) {
    for (int i = 1; i <= m; i++) {
        if (y >= abs(x)) {
            printf("U"); 
            y -= dis[i]; 
        }
        else if (y <= -abs(x)) {
            printf("D"); 
            y += dis[i]; 
        }
        else if (x <= -abs(y)) {
            printf("L"); 
            x += dis[i]; 
        }
        else {
            printf("R"); 
            x -= dis[i]; 
        }
    }

    if (x || y)
        puts("ERROR"); 

    puts(""); 
}

signed main() {
    scanf("%lld", &n); 
    for (int i = 1; i <= n; i++) {
        scanf("%lld%lld", &x[i], &y[i]); 

        if ((x[i] + y[i]) & 1) 
            flag2 = true; 
        else 
            flag1 = true; 
    }
    
    if (flag1 && flag2) {
        puts("-1"); 
        return 0; 
    }

    dis[m] = dis[m - 1] = dis[m - 2] = dis[m - 3] = 1; 
    for (int i = m - 4; i >= 1; i--)
        dis[i] = (dis[i + 1] << 1); 

    if (flag2)
        m--; 

    printf("%lld\n", m); 
    for (int i = 1; i <= m; i++) 
        printf("%lld ", dis[i]); 

    puts(""); 
    for (int i = 1; i <= n; i++) {
        LiXinLongWalking(x[i], y[i]); 
    }

    return Accepted
}