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:
n = int(input())
xy = [tuple(map(int, input().split())) for _ in range(n)]
s = set([(x + y) % 2 for x, y in xy])
if len(s) > 1:
    print(-1)
    exit(0)

d = []
w = ["" for _ in xy]
if s.pop() == 0:
    d = [1]
    w = ["L" for _ in xy]
    xy = [(x + 1, y) for x, y in xy]

b = 1
while True:
    if all(abs(x) + abs(y) == 1 for x, y in xy):
        d.append(b)
        for i in range(len(xy)):
            x, y = xy[i]
            if x > 0:
                w[i] += 'R'
            elif x < 0:
                w[i] += 'L'
            elif y > 0:
                w[i] += 'U'
            else:
                w[i] += 'D'
        break
    d.append(b)
    for i in range(len(xy)):
        x, y = xy[i]
        if x % 2 == 1:
            if y % 4 == 2 and (x - 1) % 4 == 0 or y % 4 == 0 and (x - 1) % 4 == 2:
                w[i] += 'R'
                xy[i] = ((x - 1) // 2, y // 2)
            else:
                w[i] += 'L'
                xy[i] = ((x + 1) // 2, y // 2)
        else:
            if x % 4 == 2 and (y - 1) % 4 == 0 or x % 4 == 0 and (y - 1) % 4 == 2:
                w[i] += 'U'
                xy[i] = (x // 2, (y - 1) // 2)
            else:
                w[i] += 'D'
                xy[i] = (x // 2, (y + 1) // 2)
    b *= 2

print(len(d))
print(*d)
for t in w:
    print(t)