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:
#include <bits/stdc++.h>
const int N = 1e3 + 5;
int n, a;
long long x[N], y[N], bin[33];
inline void shu(long long x, long long y) {
	for (int i = a - 1; i >= 0; i--) {
		if (std::labs(x) > std::labs(y)) {
			putchar(x < 0 ? 'L' : 'R');
			x < 0 ? x += bin[i] : x -= bin[i];
		} else {
			putchar(y < 0 ? 'D' : 'U');
			y < 0 ? y += bin[i] : y -= bin[i];
		}
	}
	puts("");
}
int main() {
	scanf("%d", &n);
	bool tf = false, tf1 = false;
	for (int i = 1; i <= n; i++) {
		scanf("%lld %lld", &x[i], &y[i]);
		((x[i] + y[i]) & 1 ? tf : tf1) = true;
	}
	if (tf && tf1) return puts("-1"), 0;
	if (tf) {
		printf("%d\n", a = 33);
		for (int i = a - 1; i >= 0; i--) 
			printf("%lld%c", bin[i] = 1LL << i, " \n"[i == 0]);
	} else {
		printf("%d\n", a = 34);
		for (int i = a - 1; i >= 1; i--) 
			printf("%lld ", bin[i] = 1LL << (i - 1));
		printf("%lld\n", bin[0] = 1);
	}
	for (int i = 1; i <= n; i++) shu(x[i], y[i]);
	return 0;
}