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:
def main():
    N = int(input())
    P = []
    distance_max = 0
    mode = 0

    for i in range(N):
        X, Y = map(int, input().split())
        distance = abs(X) + abs(Y)

        if i == 0:
            mode = distance % 2
        elif distance % 2 != mode:
            print(-1)
            return

        if mode == 0:
            X = X - 1
            distance = abs(X) + abs(Y)

        if distance > distance_max:
            distance_max = distance

        P.append((X, Y))

    d = []
    di = 1
    for i in range(40):
        if di > distance_max:
            break
        d.append(di)
        di = di * 2

    d.sort(reverse=True)

    if mode == 0:
        d.append(1)

    print(len(d))
    print(" ".join(map(str, d)))

    for p in P:
        path = ""
        x, y = p[0], p[1]
        previous = 0
        for di in d:
            if previous == di and di == 1:
                path = path + "R"
                break
            if x + y < 0:
                if x - y < 0:
                    path = path + "L"
                    x = x + di
                else:
                    path = path + "D"
                    y = y + di
            else:
                if x - y < 0:
                    path = path + "U"
                    y = y - di
                else:
                    path = path + "R"
                    x = x - di
            previous = di
        print(path)
    return

if __name__ == '__main__':
    main()