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


#合計が偶数or奇数のどちらかだけしかできない
if N != 1:
    a = abs(XY[0][0]) + abs(XY[0][1])
    flag = (XY[0][0] + XY[0][1])%2
for i in range(N-1):
    b = abs(XY[i+1][0]) + abs(XY[i+1][1])
    a = max(a, b)
    if flag != (XY[i+1][0] + XY[i+1][1])%2:
        print (-1)
        exit()

#必要な桁数の確認
m = 0
while a > 1:
    m += 1
    a = a//2

#腕の長さを求める
d = []
for i in range(m+3, -1, -1):
    d += [2 ** i]

if flag == 0: #偶数の場合一つずらすための1を加える
    print (len(d) + 1)
    print (' '.join(map(str, [1] + d)))
else: #奇数の場合そのまま出力
    print (len(d))
    print (' '.join(map(str, d)))
#ここまでで、腕の長さが決定
#これ以降で各X, Yに対する答えを見つける。

def string(X, Y): #あるXYに対して動かし方を返す
    if (abs(X) + abs(Y))%2 == 0: #偶数のとき
        ans = 'R'
        x = X - 1
        y = Y
    else:
        x, y = X, Y
        ans = str()
    for i in d:
        if abs(x - i) + abs(y) < i:
            ans += 'R'
            x = x - i
        elif abs(x + i) + abs(y) < i:
            ans += 'L'
            x = x + i
        elif abs(x) + abs(y - i) < i:
            ans += 'U'
            y = y - i
        elif abs(x) + abs(y + i) < i:
            ans += 'D'
            y = y + i
    return ans

for i in XY:
    print (string(i[0], i[1]))
# print (string(XY[0][0], XY[0][1]))
# print (string(XY[1][0], XY[1][1]))
# print (string(XY[2][0], XY[2][1]))
# print (string(XY[3][0], XY[3][1]))