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


# 各点の原点からのマンハッタン距離の偶奇は一致していなければならない
if len(set([(abs(x) + abs(y)) % 2 for x, y in Point])) == 2:
    print(-1)
    exit()


# 2べきの腕を構成
Arms = [2 ** i for i in reversed(range(39))]

# 偶数に合わせたい場合は長さ1の腕を追加
if (abs(Point[0][0]) + abs(Point[0][1])) % 2 == 0:
    Arms.append(1)


# Arm部の答えを出力
print(len(Arms))
print(' '.join(map(str, Arms)))


# 各点に到達するための腕の決める
for x, y in Point:
    ans = ''
    for length in Arms:
        min_diff, tmp_s = float('inf'), ''
        next_x, next_y = None, None
        for order, dx, dy in (('L', 1, 0), ('R', -1, 0), ('D', 0, 1), ('U', 0, -1)):
            tmp_x, tmp_y = (x + length * dx), (y + length * dy)
            diff = abs(tmp_x) + abs(tmp_y)

            if diff < min_diff:
                min_diff = diff
                tmp_s = order
                next_x, next_y = tmp_x, tmp_y

        ans += tmp_s
        x, y = next_x, next_y
    print(ans)