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 = [[int(item) for item in input().split()] for _ in range(n)]

# If mod2 changes, there are no answer
mod2 = (xy[0][0] + xy[0][1]) % 2
for x, y in xy:
    if (x + y) % 2 != mod2:
        print(-1)
        exit()

if mod2 == 1:
    print(31)
    print(" ".join([str(2**item) for item in range(31)]))
else:
    print(32)
    print("1 " + " ".join([str(2**item) for item in range(31)]))

for x, y in xy:
    if mod2 == 0:
        x -= 1
        print("R", end="")
    u = x + y
    v = x - y
    bits = [[0] * 31 for _ in range(2)]
    if u < 0:
        bits[0] = [1] * 31
        bits[0][30] = 0
    else:
        bits[0][30] = 1
    if v < 0:
        bits[1] = [1] * 31
        bits[1][30] = 0
    else:
        bits[1][30] = 1
    for i in range(30):
        if u >= 0 and abs(u)//2>>i & 1:
            bits[0][i] = 1
        if u < 0 and abs(u)//2>>i & 1:
            bits[0][i] = 0
        if v >= 0 and abs(v)//2>>i & 1:
            bits[1][i] = 1
        if v < 0 and abs(v)//2>>i & 1:
            bits[1][i] = 0
    for u_b, v_b in zip(bits[0], bits[1]):
        if u_b == 1 and v_b == 1:
            print("R", end="")
        elif u_b == 0 and v_b == 0:
            print("L", end="")
        elif u_b == 1 and v_b == 0:
            print("U", end="")
        elif u_b == 0 and v_b == 1:
            print("D", end="")
    print("")