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
import sys
try:
    from typing import List
except ImportError:
    pass


def solve(N: int, X: "List[int]", Y: "List[int]"):
    parities = {(Xi + Yi) % 2 for Xi, Yi in zip(X, Y)}
    if len(parities) > 1:
        print(-1)
        return

    d = [1 << i for i in range(39)]
    if next(iter(parities)) == 0:
        d.append(1)

    print(len(d))
    print(*d)

    x0 = -sum(d)
    for Xi, Yi in zip(X, Y):
        u = (Xi - x0 - Yi) // 2
        v = (Xi - x0 + Yi) // 2
        modes = []
        for i in range(39):
            ui = (u & (1 << i)) != 0
            vi = (v & (1 << i)) != 0
            modes.append({
                (False, False): "L",
                (False, True): "U",
                (True, False): "D",
                (True, True): "R",
            }[ui, vi])
        if len(d) > len(modes):
            modes.append("L")
        print("".join(modes))


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    X = [int()] * (N)  # type: "List[int]"
    Y = [int()] * (N)  # type: "List[int]"
    for i in range(N):
        X[i] = int(next(tokens))
        Y[i] = int(next(tokens))
    solve(N, X, Y)


if __name__ == '__main__':
    main()