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 = []
parity = {}
for _ in range(N) :
    x, y = map(int, input().split())
    point.append((x, y))
    parity[(x + y) % 2] = 1

if len(set(parity)) == 2 :
    print('-1')
else :
    m = 38
    parity = 1 if (1 in parity) else 0
    print(m + 1 - parity)
    if parity == 1 :  # 距離が奇数
        print(*[1 << i for i in range(m)])
    else :
        print(1, *[1 << i for i in range(m)])

    def arm(x, y, m) :
        if abs(x) >= abs(y) :
            if x >= 0 :
                return ('R', x - (1<<m), y)
            else :
                return ('L', x + (1<<m), y)
        else :
            if y >= 0 :
                return ('U', x, y - (1<<m))
            else :
                return ('D', x, y + (1<<m))

    for x, y in point :
        ans = []
        for i in range(m-1, -1, -1) :
            mode, x, y = arm(x, y, i)
            ans.append(mode)
        if parity == 0 :  # 偶数の場合一つ足す
            if x == 1 :
                ans.append('R')
            elif x == -1 :
                ans.append('L')
            elif y == 1 :
                ans.append('U')
            elif y == -1 :
                ans.append('D')
        print(''.join(ans[::-1]))