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:
#!/usr/bin/env python3

def main():
    N = int(input())
    XY_list = []
    for i in range(N):
        XY_list.append(list(map(int, input().split())))

    rot_list = list(map(lambda xy: [xy[0] + xy[1], -xy[0] + xy[1]], XY_list))

    f = True
    p = rot_list[0][0] % 2
    for i in range(1, N):
        if rot_list[i][0] % 2 != p:
            f = False
            break

    if not f:
        print(-1)
    else:
        offset = 2 ** 31 - p
        m = 32 - p
        d = []
        if p == 0:
            d.append(1)
        for k in range(31):
            d.append(2 ** k)
        w = []
        for i in range(N):
            uv = rot_list[i]
            u, v = uv[0] + offset, uv[1] + offset
            s = ''
            if p == 0:
                s = 'D'
            for k in range(31):
                u //= 2
                v //= 2
                u1, v1 = u % 2, v % 2
                if u1 == 0 and v1 == 0:
                    s += 'D'
                elif u1 == 0 and v1 == 1:
                    s += 'L'
                elif u1 == 1 and v1 == 0:
                    s += 'R'
                elif u1 == 1 and v1 == 1:
                    s += 'U'
            w.append(s)

        print(m)
        s = ''
        for dv in d:
            s += ' ' + str(dv)
        print(s[1:])
        for i in range(N):
            print(w[i])


if __name__ == '__main__':
    main()