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:
#!/mnt/c/Users/moiki/bash/env/bin/python
# FROM : https://atcoder.jp/contests/abc111/submissions/4032175

N = int(input())
targets = [ list(map(int, input().split())) for _ in range(N)]

mod_1st = sum(targets[0]) % 2 
if not all( sum(t) %2 == mod_1st for t in targets[1:]):
    print(-1)
    exit(0)

# if mod == 1, m = 31, di = 2^(i-1), 
# if mod == 0, m = 32, di = 2^(i-1), d32 = 1

# num of arms

mod = mod_1st
print(33 - mod)  # 33 or 32 
D = [2**i for i in range(31, -1, -1)] # 32
if mod == 0:
    D.append(1)
print(' '.join(map(str, D)))
# ----
for (x,y) in targets:
    temp = []
    u = x+y
    v = x-y
    for d in D:
        if u >= 0:
            if v >= 0:
                temp.append("R")
                u -= d
                v -= d
            elif v <  0:
                temp.append("U")
                u -= d
                v += d
        elif u < 0:
            if v >= 0:
                temp.append("D")
                u += d
                v -= d
            elif v < 0 :
                temp.append("L")
                u += d
                v += d

    # for d in D:
    #     if x >= y and x+y >= 0:
    #         temp.append("R")
    #         x -= d
    #     elif x < y and x + y >= 0:
    #         temp.append("U")
    #         y -= d
    #     elif x >= y and x + y  <0 :
    #         temp.append("D")
    #         y += d
    #     else:
    #         temp.append("L")
    #         x += d
    print(''.join(temp))