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>

using namespace std;

using ll = int64_t;
using Vi = vector<int>;
using Vl = vector<ll>;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;

constexpr int I_INF = 2147483647;
constexpr ll L_INF = 9223372036854775807LL;

//===




int main()
{
	int N;
	cin >> N;

	Vl x(N), y(N), u(N), v(N);

	for (int i = 0; i < N; ++i) {
		cin >> x[i] >> y[i];
		u[i] = x[i] + y[i];
		v[i] = x[i] - y[i];
	}

	bool is_odd = (u[0] % 2 + 2) % 2 == 1;
	for (int i = 1; i < N; ++i) {
		if (is_odd) {
			if ((u[i] % 2 + 2) % 2 == 0) {
				cout << -1 << endl;
				return 0;
			}
		}
		else {
			if ((u[i] % 2 + 2) % 2 == 1) {
				cout << -1 << endl;
				return 0;
			}
		}
	}



	int m = 31;
	if (!is_odd) ++m;
	Vl d(m);
	d[0] = 1;
	for (int i = 0; i < 30; ++i) {
		d[i + 1] = d[i] * 2;
	}
	if (!is_odd) d[31] = 1;

	cout << m << endl;
	for (int i = 0; i < m - 1; ++i) {
		cout << d[i] << " ";
	}
	cout << d[m - 1] << endl;



	if (!is_odd) {
		for (int i = 0; i < N; ++i) {
			--u[i]; --v[i];
		}
	}

	ll ma = d[30] * 2;

	for (int i = 0; i < N; ++i) {
		string mnp;
		ll au, av;
		au = (u[i] + ma - 1) / 2;
		av = (v[i] + ma - 1) / 2;
		for (int j = 0; j < 31; ++j) {
			bool bu, bv;
			bu = au & (1 << j);
			bv = av & (1 << j);
			if (!bu && !bv) mnp += 'L';
			else if (bu && bv) mnp += 'R';
			else if (!bu && bv) mnp += 'D';
			else if (bu && !bv) mnp += 'U';
		}
		if (!is_odd) mnp += 'R';

		cout << mnp << endl;
	}

	return 0;
}