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:
ri = lambda: int(input())
rl = lambda: list(map(int,input().split()))
rr = lambda N: [ri() for _ in range(N)]
YN = lambda b: print('YES') if b else print('NO')
yn = lambda b: print('Yes') if b else print('No')
OE = lambda x: print('Odd') if x%2 else print('Even')
INF = 10**18

N=ri()
U=[0]*N #u = x + y
V=[0]*N #v = x - y
parity = 0
for i in range(N):
    x,y = rl()
    U[i],V[i] = format(x+y,'+032b'), format(x-y,'+032b')
    parity += (x+y)%2

if parity == 0 or parity == N:
    parity //= N
    m = 31 if parity else 32
    print(m)
    d = [1 for i in range(m)]
    for i in range(1,31):
        d[i] = d[i-1]*2
    d.sort(reverse=True)
    print(*d, sep=' ')

    for i in range(N):
        res = ''
        u,v = U[i],V[i]

        ub,vb = [1]+list(map(int,u[1:-1])), [1]+list(map(int,v[1:-1]))
        if not parity:
            ub += [0]
            vb += [0]
        if u[0] == '-': ub = list(map(lambda x: x^1, ub))
        if v[0] == '-': vb = list(map(lambda x: x^1, vb))

        for ub_,vb_ in zip(ub,vb):
            if ub_==0 and vb_==0:
                res += 'L'
            elif ub_==1 and vb_==1:
                res += 'R'
            elif ub_==0 and vb_==1:
                res += 'D'
            else:
                res += 'U'
        print(res)
else:
    print(-1)