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 PYTHON3):

Solution:
from math import *

def L(xi, di):
    return xi - di

def R(xi, di):
    return xi + di

def D(yi, di):
    return yi - di

def U(yi, di):
    return yi + di

def main():
    N = int(input())
    x_list = [list(map(int, input().split())) for i in range(N)]
    sum_list = [x[0] + x[1] for x in x_list]
    checker = sum_list[0] % 2

    for wa in sum_list:
        if wa % 2 != checker:
            print("-1")
            return

    arm_list = []
    if checker == 0:
        arm_list.append(1)

    pow_i = 0
    max_sum = max(sum_list)
    while max_sum > sum(arm_list):
        arm_list.append(2 ** pow_i)
        pow_i += 1
    arm_list = sorted(arm_list, key=lambda x: -x)
    print(len(arm_list))
    print(" ".join(map(str, arm_list)))

    for c in x_list:
        now_c = [0,0]
        order = ""

        for arm in arm_list:
            dx = c[0] - now_c[0]
            dy = c[1] - now_c[1]

            if abs(dx) > abs(dy):
                if dx > 0:
                    order += "R"
                    now_c[0] = R(now_c[0], arm)
                else:
                    order += "L"
                    now_c[0] = L(now_c[0], arm)
            else:
                if dy > 0:
                    order += "U"
                    now_c[1] = U(now_c[1], arm)
                else:
                    order += "D"
                    now_c[1] = D(now_c[1], arm)
        print(order)

if __name__ == "__main__":
    main()