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

# (x + y) % 2 が全部同じじゃなかったらどう頑張ってもむり
if len(set([(x + y) % 2 for x, y in zip(X, Y)])) != 1:
    print(-1)
    exit()


def directions_str(fx, fy, tx, ty, arm):
    if fx == tx and fy == ty:
        return ''
    if abs(fx - arm - tx) + abs(fy - ty) < arm:
        return 'L' + directions_str(fx=fx - arm, fy=fy, tx=tx, ty=ty, arm=arm // 2)
    if abs(fx + arm - tx) + abs(fy - ty) < arm:
        return 'R' + directions_str(fx=fx + arm, fy=fy, tx=tx, ty=ty, arm=arm // 2)
    if abs(fx - tx) + abs(fy - arm - ty) < arm:
        return 'D' + directions_str(fx=fx, fy=fy - arm, tx=tx, ty=ty, arm=arm // 2)
    if abs(fx - tx) + abs(fy + arm - ty) < arm:
        return 'U' + directions_str(fx=fx, fy=fy + arm, tx=tx, ty=ty, arm=arm // 2)


# 全部 (x + y) % 2 == 1 なら、2^n, 2^(n-1), ..., 2, 1 って腕を作れば (x+y) <= 2^(n+1)-1 まではどこでも行ける。
# 全部 (x + y) % 2 == 0 なら、上記から 1 だけ伸ばせばどこでも行ける。
arms = []
for n in range(39):
    arms.append(2 ** n)
    if 2 ** n > 10 ** 9:
        break
arms.sort(reverse=True)

if (X[0] + Y[0]) % 2 == 1:
    print(len(arms))
    print(' '.join(map(str, arms)))
    for x, y in zip(X, Y):
        print(directions_str(fx=0, fy=0, tx=x, ty=y, arm=arms[0]))
else:
    arms.append(1)
    print(len(arms))
    print(' '.join(map(str, arms)))
    for x, y in zip(X, Y):
        print(directions_str(fx=0, fy=0, tx=x, ty=y + 1, arm=arms[0]) + 'D')