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:
# -*- coding: utf-8 -*-
import math


def binary(n, m):
    lst = []
    while n != 0:
        lst.append(n % 2)
        n = n // 2
    lst = lst + [0] * (m - len(lst))
    return list(reversed(lst))


def calc(u, v, m):
    result = ""
    u_binary = binary(u, m)
    v_binary = binary(v, m)
    for i in range(m):
        if u_binary[i] == 1 and v_binary[i] == 1:
            result += "R"
        elif u_binary[i] == 0 and v_binary[i] == 0:
            result += "L"
        elif u_binary[i] == 1 and v_binary[i] == 0:
            result += "U"
        else:
            result += "D"
    return result


U = []
V = []
N = int(input())
even, odd = 0, 0
M = 0
for p in range(N):
    x, y = map(int, input().split())
    u = x + y
    v = x - y
    U.append(u)
    V.append(v)
    M = max(M, abs(u), abs(v))
    if (x + y) % 2 == 0:
        even += 1
    else:
        odd += 1

if even >= 1 and odd >= 1:
    print(-1)

else:
    m = math.floor(math.log2(M)) + 1 if M != 0 else 1
    lst = [2 ** i for i in range(m-1, -1, -1)]
    if odd == 0:
        lst.append(1)
    print(len(lst))
    print(" ".join(map(str, lst)))
    for u, v in zip(U, V):
        u = (u + 2 ** m - 1) // 2
        v = (v + 2 ** m - 1) // 2
        print(calc(u, v, m)+"R" if odd == 0 else calc(u, v, m))