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 sys
input = sys.stdin.readline
INF = float('inf')


def inpl(): return list(map(int, input().split()))


def move_uv(x, y):
    ut = x + y
    vt = x - y
    command = ''
    u, v = 0, 0
    for i in range(len(D)):
        if u <= ut and v <= vt:
            command += 'R'
            u += D[i]
            v += D[i]
        elif u <= ut and v > vt:
            command += 'U'
            u += D[i]
            v -= D[i]
        elif u > ut and v <= vt:
            command += 'D'
            u -= D[i]
            v += D[i]
        else:
            command += 'L'
            u -= D[i]
            v -= D[i]

    return command


N = int(input())
point = []
max_length = 0
for i in range(N):
    x, y = inpl()
    max_length = max(max_length, abs(x) + abs(y))
    point.append([x, y])

parity = sum(point[0]) % 2
judge = True
for p in point:
    if parity ^ sum(p) % 2:
        judge = False
        break

if not judge:
    print(-1)
else:
    D = [2 ** i for i in range(len(bin(max_length)) - 1)]
    D.reverse()

    # X + Yが偶数の時は長さ1の腕を足す
    if parity == 0:
        D.append(1)
    print(len(D))
    print(' '.join(map(str, D)))
    for i in range(N):
        print(move_uv(point[i][0], point[i][1]))