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:
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

#A
def A():
    n = S()
    for i in n:
        if i == "1":
            print(9,end = "")
        else:
            print(1,end = "")
    print()
#B
def B():
    n = I()
    for i in range(n,1000):
        if i%111 == 0:
            print(i)
            quit()
    return

#C
def C():
    return

#D
def D():
    n = I()
    p = LIR(n)
    b = []
    for i in range(n):
        x,y = p[i]
        for j in range(i):
            s,t = p[j]
            if (abs(x-s)+abs(y-t))%2:
                print(-1)
                return
    ans = []
    for i in range(n):
        f = 0
        x,y = p[i]
        if not (x+y)%2:
            x -= 1
            if not ans:
                ans.append(1)
        if x < 0:
            x = -x
            f |= 1
        if y < 0:
            y = -y
            f |= 2
        bx = list(map(int, bin(x)[2:]))
        by = list(map(int, bin(y)[2:]))
        bx = bx[::-1]
        by = by[::-1]
        for _ in range(39-len(bx)):
            bx.append(0)
        for _ in range(39-len(by)):
            by.append(0)
        b.append([bx,by,f])
    for i in range(39):
        ans.append(1<<i)
    v = [[] for i in range(n)]
    for i in range(n):
        x,y,f = b[i]
        if x[0]:
            p = 1
            v[i].append(0)
        else:
            p = 0
            v[i].append(1)
        for j in range(1,39):
            if p:
                if x[j]:
                    if y[j]:
                        v[i][-1] ^= 3
                        k = j+1
                        while x[k]:
                            x[k] ^= 1
                            k += 1
                        x[k] = 1
                        v[i].append(1)
                        p = 0
                    else:
                        v[i].append(0)
                else:
                    if y[j]:
                        v[i].append(1)
                        p = 0
                    else:
                        v[i][-1] ^= 3
                        v[i].append(0)
            else:
                if y[j]:
                    if x[j]:
                        v[i][-1] ^= 3
                        k = j+1
                        while y[k]:
                            y[k] ^= 1
                            k += 1
                        y[k] = 1
                        v[i].append(0)
                        p = 1
                    else:
                        v[i].append(1)
                else:
                    if x[j]:
                        v[i].append(0)
                        p = 1
                    else:
                        v[i][-1] ^= 3
                        v[i].append(1)
        for j in range(39):
            if v[i][j] in [0,3]:
                if f&1:
                    v[i][j]^=3
            else:
                if f&2:
                    v[i][j]^=3
    p = ["R","U","D","L"]
    print(len(ans))
    print(*ans)
    for i in v:
        if len(ans) == 40:
            print("R",end = "")
        for j in i:
            print(p[j],end = "")
        print()
    return

#E
def E():
    return

#F
def F():
    return

#G
def G():
    return

#H
def H():
    return

#Solve
if __name__ == "__main__":
    D()