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:
import sys


# 一つ前の座標と、方向を返す
def f(x, y, i):
    d = 1 << i
    if y > x and y > -x:
        return x, y - d, "U"
    elif y < x and y > -x:
        return x - d, y, "R"
    elif y < x and y < -x:
        return x, y + d, "D"
    else:
        return x + d, y, "L"


N = int(input())
X = []
Y = []
mx = 0
for i in range(N):
    x, y = [int(x) for x in input().split()]
    mx = max(abs(x) + abs(y), mx)
    X.append(x)
    Y.append(y)

s = (X[0] + Y[0]) % 2
for i in range(N):
    if s != (X[i] + Y[i]) % 2:
        print(-1)
        sys.exit(0)

# s == 1 のとき：D:[1,2,4,8,...]
# s == 0 のとき：D:[1,1,2,4,8,...]

if s == 0:
    X = [x - 1 for x in X]

D = []
d = 1
while d < mx:
    D.append(d)
    d = d * 2

m = len(D)
print(m if s != 0 else m + 1)
if s == 0:
    D = [1] + D
print(" ".join([str(d) for d in D]))

for i in range(N):
    x, y = X[i], Y[i]
    dirs = []
    for j in range(m - 1, -1, -1):
        x, y, dir = f(x, y, j)
        dirs.append(dir)
    if s == 0:
        dirs.append("R")
    print("".join(dirs[::-1]))