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

def f(s,t):
    if s>=t and -s<=t:
        return 0
    elif s<=t and -s<=t:
        return 1
    elif s<=t and -s>=t:
        return 2
    else:
        return 3

n=int(input())
xy=[list(map(int,input().split())) for i in range(n)]
for i in range(1,n):
    if sum(xy[i])%2!=sum(xy[i-1])%2:
        print(-1)
        sys.exit()
        
data_1=["R","U","L","D"]
data_2=[[1,0],[0,1],[-1,0],[0,-1]]
    
arms=[2**i for i in range(32)]

if sum(xy[0])%2==1:
    print(len(arms))
    print(*arms)
    for X,Y in xy:
        x,y=X,Y
        ans=[]
        i=31
        while i>=0:
            c=f(x,y)
            ans.append(data_1[c])
            x-=arms[i]*data_2[c][0]
            y-=arms[i]*data_2[c][1]
            i-=1
        print("".join(ans[::-1]))
else:
    arms=[1]+arms
    print(len(arms))
    print(*arms)
    for X,Y in xy:
        x,y=X,Y
        ans=[]
        i=32
        while i>=1:
            c=f(x,y)
            ans.append(data_1[c])
            x-=arms[i]*data_2[c][0]
            y-=arms[i]*data_2[c][1]
            i-=1
        if x==1:
            ans.append("R")
        elif x==-1:
            ans.append("L")
        elif y==1:
            ans.append("U")
        else:
            ans.append("D")
        print("".join(ans[::-1]))