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;
const int maxn = 1234;
long long md2(long long v){
	v %= 2;
	if(v < 0) v += 2;
	return v;
}
long long x[maxn], y[maxn];
bool inside(long long x, long long y, int k){
	if(k == -1) return x == 0 && y == 0;
	if(md2(x) == md2(y)) return false;
	int v = 1<<(k+1); v--;
	return -v <= x && x <= v && -v <= y && y <= v && abs(x) + abs(y) <= v;
}
int main(){
	int n; cin >> n;
	for(int i = 0; i < n; i++) cin >> x[i] >> y[i];
	for(int i = 1; i < n; i++) if(md2(x[i] + y[i]) != md2(x[0] + y[0])) return !printf("-1\n");
	bool add = false;
	if(md2(x[0] + y[0]) == 0){
		add = true;
		for(int i = 0; i < n; i++) x[i] += 1;
	}
	const int bits = 31;
	cout << bits + add << endl;
	for(int i = 0; i < bits; i++) cout << (1<<i) << " "; 
	if(add) cout << 1;
	cout << endl;
	for(int i = 0; i < n; i++){
		long long cx = x[i], cy = y[i];
		string mvs;
		for(int j = bits - 1; j >= 0; j--){
			if(inside(cx - (1<<j), cy, j - 1)){
				cx -= 1<<j;
				mvs.push_back('R');
			} else if(inside(cx + (1<<j), cy, j - 1)){
				cx += 1<<j;
				mvs.push_back('L');
			} else if(inside(cx, cy - (1<<j), j - 1)){
				cy -= 1<<j;
				mvs.push_back('U');
			} else if(inside(cx, cy + (1<<j), j - 1)){
				cy += 1<<j;
				mvs.push_back('D');
			} else {
				assert(0);
			}
		}	
		reverse(mvs.begin(), mvs.end());
		if(add) mvs.push_back('L');
		long long myx = 0, myy = 0;
		for(int j = 0; j < bits; j++){
			if(mvs[j] == 'L') myx -= 1<<j;
			if(mvs[j] == 'R') myx += 1<<j;
			if(mvs[j] == 'U') myy += 1<<j;
			if(mvs[j] == 'D') myy -= 1<<j;
		}
		if(add) myx -= 1;
		cout << mvs << endl;
	}
	return 0;
}