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())
Q = [list(map(int, input().split())) for i in range(N)]

# 全体の偶奇が一致しているか
tmp = set()
for X, Y in Q:
    tmp.add((X + Y) % 2)
if len(tmp) != 1:
    print(-1)
    exit()

# 2べきの腕を用意
D = [2 ** i for i in range(30, -1, -1)]

# 偶数なら長さ1の腕を一本追加しておく
if 0 in tmp:
    D.append(1)

# 答えを作る
print(len(D))
print(" ".join(map(str, D)))

move = [(1, 0, "R"), (-1, 0, "L"), (0, 1, "U"), (0, -1, "D")]
for X, Y in Q:
    nx, ny = 0, 0
    ans = ""
    for d in D:
        tmp_move_ans = ""
        tmp_move = None
        min_move_cost = float('inf')
        for mx, my, s in move:
            cost = abs(nx + mx * d - X) + abs(ny + my * d - Y)
            if cost < min_move_cost:
                tmp_move_ans = s
                min_move_cost = cost
                tmp_move_x = mx
                tmp_move_y = my

        ans += tmp_move_ans
        nx, ny = nx + tmp_move_x * d, ny + tmp_move_y * d
    print(ans)