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:
# Python3 (3.4.3)
import sys
input = sys.stdin.readline

# -------------------------------------------------------------
# function
# -------------------------------------------------------------


# -------------------------------------------------------------
# main
# -------------------------------------------------------------
N = int(input())
XY = [list(map(int,input().split())) for _ in range(N)]

# x + y のパリティが同一かチェック, 異なる座標が存在する場合は実現不可能
p = set()
for i in range(N):
    p.add((XY[i][0] + XY[i][1]) % 2)
if len(p) > 1:
    print(-1)
    sys.exit()

# 腕の長さを1,2,4,8... で考えると, パリティ1を実現できる.
# 与えられた座標のパリティが0の場合, X座標を-1し, パリティ1の場合に帰着する(あとでX+1する)
if 0 in p:
    for i in range(N):
        XY[i][0] -= 1

# アームを準備
D = []
for i in range(35):
    D.append(2**i)
D.sort(reverse=True)

Ans = []
# 順番に計算
for i in range(N):
    x,y = XY[i][0],XY[i][1]
    x0,y0 = 0,0
    ans = ""
    # 原点を中心にX字で分割される領域の (上下左右) どちらかを判断し, 移動させ, 都度原点を調整
    for d in D:
        dx,dy = x-x0,y-y0
        # 右
        if dy < dx and dy > -dx:
            ans += "R"
            x0 += d
        # 下
        elif dy < dx and dy < -dx:
            ans += "D"
            y0 -= d
        # 左
        elif dy > dx and dy < -dx:
            ans += "L"
            x0 -= d
        # 上
        else:
            ans += "U"
            y0 += d
    Ans.append(ans)

# パリティが 0 の場合 : 長さ1のアームを追加, X座標を -1 した分を +1 して調整(つまり最後に "R" を追加する)
if 0 in p:
    D.append(1)
    print(len(D))
    print(" ".join(map(str,D)))
    for ans in Ans:
        print(ans + "R")
# パリティが 1 の場合 : そのまま出力
else:
    print(len(D))
    print(" ".join(map(str,D)))
    for ans in Ans:
        print(ans)