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 <cstdio>
#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <functional>

using namespace std;
typedef long long int ll;

#define repi(i,a,b) for(ll i=a;i<b;i++)
#define rep(i,a) repi(i,0,a)
#define rrep(i,a) for(ll i=a-1;i>=0;i--)

int main(){
  ll N;
  cin >> N;
  ll query[N][2];
  rep(i, N) scanf("%lld %lld", query[i], query[i]+1);

  ll odd = ((query[0][0] + query[0][1]) % 2 + 2) % 2;
  rep(i, N){
    if(((query[i][0] + query[i][1]) % 2 + 2) % 2 != odd){
      odd = -1;
      break;
    }
  }

  if(odd == -1){
    cout << -1 << endl;
  }
  else{
    const ll m = 31;
    cout << (m + 1 - odd) << endl;
    ll powm = 1;
    powm <<= m;
    ll d = 1;
    if(!odd) printf("%d ", 1);
    rep(i, m-1){
      printf("%lld ", d);
      d <<= 1;
    }
    printf("%lld\n", d);

    rep(i, N){
      ll u = (query[i][0] + query[i][1] + powm - odd) / 2;
      ll v = (query[i][0] - query[i][1] + powm - odd) / 2;
      ll mask = 1;
      if(!odd) cout << 'L';
      rep(i, m){
        if(!(u & mask) && !(v & mask)) cout << 'L';
        if((u & mask) && (v & mask)) cout << 'R';
        if(!(u & mask) && (v & mask)) cout << 'D';
        if((u & mask) && !(v & mask)) cout << 'U';
        mask <<= 1;
      }
      cout << endl;
    }
  }
  return 0;
}