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())
x = [0 for i in range(0, n)]
y = [0 for i in range(0, n)]

for i in range(0, n):
    x[i], y[i] = [int(i) for i in input().split(" ")]

mod2 = (x[0] + y[0]) % 2
imp = False

for i in range(1, n):
    if (x[i] + y[i]) % 2 != mod2:
        print(-1)
        imp = True
        break
        
if not imp:
    if mod2 == 0:
        x = [i + 1 for i in x]

    u = [x[i] + y[i] for i in range(0, n)]
    v = [x[i] - y[i] for i in range(0, n)]

    mode = ["L", "D", "U", "R"]
    m = 31

    if mod2 == 0:
        print(m + 1)
        print("1 " + " ".join([str(2**(i - 1)) for i in range(1, m + 1)]))
    else:
        print(m)
        print(" ".join([str(2**(i - 1)) for i in range(1, m + 1)]))

    for i in range(0, n):
        w = ""
        if mod2 == 0:
            w = "L"
        ui = (u[i] + 2**m - 1) // 2
        vi = (v[i] + 2**m - 1) // 2
        for l in range(0, m):
            ul = ui % 2
            ui = ui // 2
            vl = vi % 2
            vi = vi // 2
            w += mode[ul * 2+ vl]
        print(w)