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:
import sys, math, collections, heapq, itertools
def gcd(a, b):
    a, b = max(a, b), min(a, b)
    while a % b > 0: a, b = b, a % b
    return b
  
def solve():
    file = sys.stdin.readline #single: int(file()), line: map(int, file().split())
    N = int(file())
    point = [[int(i) for i in file().split()] for j in range(N)]
    length = (point[0][0] + point[0][1]) % 2
    for i in range(1, N):
        if sum(point[i]) % 2 != length:
            print(-1)
            break
    else:
        d = [pow(2, i) for i in range(31)]
        direction = {("0", "0"): "L", ("1","1"): "R", ("0", "1"): "D", ("1", "0"): "U"}
        ans = ""
        add = (0 if length == 1 else 1)
        if add == 1: d.append(1)
        for i in range(N):
            U, V = point[i][0] + point[i][1] + add, point[i][0] - point[i][1] + add
            ubit = format((U + pow(2, 31) - 1)//2, "b").zfill(31)
            vbit = format((V + pow(2, 31) - 1)//2, "b").zfill(31)
            arm = ""
            for j in reversed(range(31)):
                arm += direction[(ubit[j], vbit[j])]
            if add == 1: arm += "L"
            ans += arm + "\n"
        print(len(d))
        print(" ".join(map(str, d)))
        print(ans)

    INF = 10 ** 25
    mod = 7 + 10 ** 9
    return 0
  
if __name__ == "__main__":
    solve()