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:
# 解説を参考に作成
# import sys
# sys.setrecursionlimit(10 ** 6)
# import bisect
# from collections import deque
# from decorator import stop_watch
#
#
# @stop_watch
def solve(N, XY):
    tmp = 0
    for x, y in XY:
        tmp += (abs(x) + abs(y)) % 2
    if tmp % N != 0:
        print(-1)
        return
    import math
    m = math.ceil(math.log2(2 * 10 ** 9)) + 1
    d = [2 ** (m - i) for i in range(m)] + [1]
    d += [1] if tmp == 0 else []
    m = len(d)
    w = []
    for xi, yi in XY:
        xx = 0
        yy = 0
        W = ''
        for di in d:
            if abs(xi - xx) >= abs(yi - yy):
                if xx <= xi:
                    xx += di
                    W += 'R'
                else:
                    xx -= di
                    W += 'L'
            else:
                if yy <= yi:
                    yy += di
                    W += 'U'
                else:
                    yy -= di
                    W += 'D'
        w.append(W)
    print(m)
    print(' '.join([str(i) for i in d]))
    [print(wi) for wi in w]


if __name__ == '__main__':
    # S = input()
    N = int(input())
    # N, M = map(int, input().split())
    # A = [int(i) for i in input().split()]
    # B = [int(i) for i in input().split()]
    XY = [[int(i) for i in input().split()] for _ in range(N)]
    solve(N, XY)

    # # test
    # from random import randint
    # from func import random_str
    # solve()