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:
# できなかった
# アームの長さが決まると(xm+ym)mod2は一定になる、これが一定でなければ無理
# (xj+yj)mod2=1としてよい、長さ1の腕を追加することで0の場合も考えられる
# (u,v)=(x+y,x-y)(回転座標)とすると、ui,viをu(i+1),v(i+1)から独立に決定できる(+d,-dいづれかはされることが確定している)
# よってdiを決めたときにui,viを決める問題をu,vについて独立に解けば、各関節の向きを決定できる
# u(i+1)=ui+diとなるi∈{1,...,m}の集合をSとすると、u(m)=-Σ(1≦i≦m) di +Σ(i∈S) 2di が成り立つ
# -2*10^9≦Uj,Vj≦2*10^9 と 1≦m≦40 より m=31,di=2^(i-1) とできる。すると、Uj=-(2^31-1) +Σ(i∈S) 2di となる
# つまりΣ(i∈S) 2di =Uj+(2^31-1) となるようにSを選ぶことができるので解ける

n=int(input())
listXY=[list(map(int,input().split())) for _ in range(n)]
listUV=[[listXY[i][0]+listXY[i][1],listXY[i][0]-listXY[i][1]]for i in range(n)]

isOdd=listUV[0][0]%2
canReach=1
for i in range(1,n):
    if isOdd!=listUV[i][0]%2:
        canReach=0
        break

if not canReach:
    print(-1)
else:
    offset=2**31-isOdd
    m=32-isOdd
    d=[2**i for i in range(32)]
    w=[]
    for i in range(n):
        x,y=0,0
        u,v=listUV[i][0]+offset,listUV[i][1]+offset
        s=''
        if not isOdd:
            s='L'
            x=x-1
        for k in range(31):
            u //= 2
            v //= 2
            u1, v1 = u % 2, v % 2
            # L(-d,-d),R(+d,+d),D(-d,+d),U(+d,-d)
            if u1 == 0 and v1 == 1:
                s += 'D'
                y=y-d[k]
            elif u1 == 0 and v1 == 0:
                s += 'L'
                x=x-d[k]
            elif u1 == 1 and v1 == 1:
                s += 'R'
                x=x+d[k]
            elif u1 == 1 and v1 == 0:
                s += 'U'
                y=y+d[k]
        w.append(s)
        # print(x,y,s)
    # print(listXY)
    # print(listUV)
    print(32-isOdd)
    s=''
    if not isOdd:
        s='1 '
    for i in range(31):
        s+=str(d[i])+' '
    print(s)
    for i in range(n):
        print(w[i])