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:
from sys import exit
N = int(input())

Od = True
Ev = True
XY = []
for _ in range(N):
    x, y = map(int, input().split())
    if (x+y) % 2:
        Ev = False
    else:
        Od = False
    XY.append((x, y))

if not Od and not Ev:
    print(-1)
    exit()

ans = [2**i for i in range(31)]
Sig = sum(ans)

if Ev:
    ans = [1] + ans
print(len(ans))
print(*ans)
for x, y in XY:
    if Ev:
        x -= 1
    pl = abs((Sig - (x + y))//2)
    mi = abs((Sig - (x - y))//2)
    RU = [1 if pl & 2**i else 0 for i in range(31)]
    RD = [1 if mi & 2**i else 0 for i in range(31)]
    ans = [None]*31
    for j in range(31):
        if RU[j] and RD[j]:
            ans[j] = 'R'
        elif RD[j] and not RU[j]:
            ans[j] = 'D'
        elif not RD[j] and RU[j]:
            ans[j] = 'U'
        else:
            ans[j] = 'L'
    ans = ''.join(ans)
    xi, yi = 0, 0
    for i, s in enumerate(ans):
        if s == 'U':
            yi += 2**i
        if s == 'D':
            yi -= 2**i
        if s == 'R':
            xi += 2**i
        if s == 'L':
            xi -= 2**i
    if y != yi:
        ans = ans.translate(str.maketrans('UD', 'DU'))
    if x != xi:
        ans = ans.translate(str.maketrans('LR', 'RL'))
    if Ev:
        ans = 'R' + ans
    print(ans)