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:
def solve(x, y, d, m):
    ret = ""
    dx = [-1, 0, 0, 1]
    dy = [0, -1, 1, 0]
    mode = ['R', 'U', 'D', 'L']
    for i in range(m):
        dir = 0
        t = abs(x + d[i] * dx[0]) + abs(y + d[i] * dy[0])
        for j in range(4):
            nx = x + d[i] * dx[j]
            ny = y + d[i] * dy[j]
            if abs(nx) + abs(ny) < t:
                t = abs(nx) + abs(ny)
                dir = j
        x = x + d[i] * dx[dir]
        y = y + d[i] * dy[dir]
        ret += mode[dir]

    print (ret)


def main():
    m = 34
    X, Y, d = [], [], []

    for i in range(32, 0, -1):
        d += [2**i]
    d += [1]

    N = int(input())
    even, odd = 0, 0

    for i in range(N):
        x, y = map(int, input().split())
        X += [x]; Y += [y]

        if (abs(x) + abs(y)) % 2 == 0:
            even += 1
        else:
            odd += 1

    if even and odd:
        print(-1)
        return 0

    if odd:
        m -= 1
    else:
        d += [1]

    print(m)
    print(" ".join(map(str, d)))

    for i in range(N):
        solve(X[i], Y[i], d, m)

main()