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:
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
    n=int(input())
    XY=[tuple(map(int,input().split())) for _ in range(n)]
    parity=[0]*2
    for x,y in XY:
        parity[(x+y)%2]=1

    # それぞれのパリティの点が存在すると不可能
    if(parity[0] and parity[1]):
        print(-1)
        return

    m=31
    D=[pow(2,i) for i in range(m)]
    # 偶数の場合は奇数に帰着させる
    if(parity[0]):
        XY=[(x-1,y) for x,y in XY]
        D=[1]+D

    U=[x-y for x,y in XY]
    V=[x+y for x,y in XY]

    W=[0]*n
    for j in range(n):
        res=[0]*m
        u=(U[j]+pow(2,m)-1)//2
        v=(V[j]+pow(2,m)-1)//2
        for i in range(m):
            ub=u&1; vb=v&1
            if(ub and vb):
                res[i]='R'
            elif(ub and (not vb)):
                res[i]='D'
            elif((not ub) and vb):
                res[i]='U'
            else:
                res[i]='L'
            u>>=1; v>>=1
        ans=''.join(res)
        W[j]=ans

    m=m+parity[0]
    print(m)
    print(*D)
    for j in range(n):
        ans=W[j] if(parity[1]) else 'R'+W[j]
        print(ans)
resolve()