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 CPP):

Solution:
//Created Time:2020年03月19日 星期四 14时11分16秒
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define N 1003

using namespace std;

int n;
int x[N], y[N];

int main(){
	scanf("%d", &n); bool flag;
	for(int i = 1; i <= n; ++i){
		scanf("%d%d", x + i, y + i);
		if(i == 1) flag = abs(x[i]) + abs(y[i]) & 1;
		else if((abs(x[i]) + abs(y[i]) & 1) != flag) return puts("-1"), 0;
	}
	int m = 31;
	cout << m + (!flag) << endl;
	for(int i = 0; i < m; ++i) cout << (1ll << m - i - 1) << ' ';
	if(!flag) cout << 1; cout << endl;
	for(int i = 1; i <= n; ++i){
		long long nx = 0, ny = 0;
		if(!flag) --x[i];
		for(int j = 0; j < m; ++j){
			long long tmp, d = 1 << m - 1 - j, mn = 2147483647;
			if(abs(nx + d - x[i]) + abs(ny - y[i]) < mn)
				mn = abs(nx + d - x[i]) + abs(ny - y[i]), tmp = 0;
			if(abs(nx - d - x[i]) + abs(ny - y[i]) < mn)
				mn = abs(nx - d - x[i]) + abs(ny - y[i]), tmp = 1;
			if(abs(nx - x[i]) + abs(ny + d - y[i]) < mn)
				mn = abs(nx - x[i]) + abs(ny + d - y[i]), tmp = 2;
			if(abs(nx - x[i]) + abs(ny - d - y[i]) < mn)
				mn = abs(nx - x[i]) + abs(ny - d - y[i]), tmp = 3;
			switch(tmp){
				case 0:
					nx += d, putchar('R'); break;
				case 1:
					nx -= d, putchar('L'); break;
				case 2:
					ny += d, putchar('U'); break;
				case 3:
					ny -= d, putchar('D'); break;
			}
		}
		if(!flag) putchar('R'); putchar('\n');
//		cout << nx << ' ' << ny << endl;
	}
	return 0;
}