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:
# http://tutuz.hateblo.jp/entry/2018/12/09/220715

inf = float('inf')

n = int(input())
coordinates = [tuple(map(int, input().split())) for _ in range(n)]

parity = None
can_make = True
for coordinate in coordinates:
    if parity is None:
        parity = sum(coordinate) % 2
    else:
        if parity != sum(coordinate) % 2:
            can_make = False
            break

if not can_make:
    print(-1)
    exit()
    # 到達可能な頂点はxy座標の和のパリティが一致している必要がある

if parity == 0:
    d = [pow(2, i) for i in range(31 + 1)] + [1]
    # 奇数は1だけなので、1を追加して、全ての腕の合計が偶数になるようにする
else:
    d = [pow(2, i) for i in range(31 + 1)]
    # 奇数は1だけなので、全ての腕の合計は奇数になる
d.sort(reverse=True)

ans = []
for x, y in coordinates:
    u = x + y
    v = x - y
    # 45度回転する
    # u,vの最大値はx,yの2倍=2*10**9
    # 2 ** 31 > 2 * (10 ** 9) なので、2**31までの二冪で大丈夫そう
    # [1, 2, ..., 2 ** 31]
    # L(-d,-d)R(+d,+d)U(+d,-d)D(-d,+d)
    # なので、一つのdで、uでは加算、vでは減算などでき、二冪一セットで足りる
    curu, curv = 0, 0
    ops = ''
    for dd in d:
        dist = inf
        op = ''
        det_du, det_dv = 0, 0
        for c, (du, dv) in zip('LRDU', [(-1, -1), (1, 1), (-1, 1), (1, -1)]):
            t = abs(curu + du * dd - u) + abs(curv + dv * dd - v)
            if dist > t:
                op = c
                dist = t
                det_du = du
                det_dv = dv
        ops += op
        curu += det_du * dd
        curv += det_dv * dd
    if (curu, curv) == (u, v):
        ans.append(ops)
    else:
        print(-1)
        # print('不一致', curx, cury, x, y)

print(len(d))
print(*d)
print(*ans, sep='\n')