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
#結局よくわからず解法見てしもた
#通ったし今度はリファクタリングや

def 解():
    iN = int(input())
    aP = [[int(_) for _ in sLine.rstrip("\n").split()] for sLine in sys.stdin.readlines()]

    iMod = sum(aP[0]) % 2
    for i in range(1,iN):
        if sum(aP[i]) % 2 != iMod :
            print("-1")
            exit()

    i最遠 = max([ abs(iX)+abs(iY) for iX , iY in aP])

    a腕 = [1]
    if iMod == 0 :
        a腕 = [1,1]

    for i in range(32):
        a腕.append(a腕[-1] * 2)
        if i最遠 // 2 < a腕[-1]:
            break

    a腕.reverse()
    iLen腕 = len(a腕)
    aRet = []
    for iX,iY in aP:
        aCommand=[]
        for i in range(iLen腕):
            if abs(iX) > abs(iY):
                if iX < 0 :
                    iX += a腕[i]
                    aCommand.append("L")
                else:
                    iX -= a腕[i]
                    aCommand.append("R")
            else:
                if iY < 0 :
                    iY += a腕[i]
                    aCommand.append("D")
                else:
                    iY -= a腕[i]
                    aCommand.append("U")
        aRet.append("".join(aCommand))

    print(iLen腕)
    print(" ".join([str(_) for _ in a腕]))
    sys.stdout.write("\n".join(aRet) + "\n")

if __name__ == '__main__':
    解()