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>
#define REP(i,n) for(ll i = 0; i < (ll)n; i++)
#define FOR(i,a,b) for (ll i=(a);i<(ll)b; i++)
#define ALL(obj) (obj).begin(),(obj).end()
#define INF 1000000000000000
using namespace std;
typedef long long ll;
typedef pair<long long, long long> pll;
typedef double db;
typedef string str;
typedef pair<ll,ll> p;
const int MOD = 1000000007;


int main(){
    int N;cin>>N;
    vector<pll> pos(N);
    for(int i = 0; i <N; i++) cin>>pos[i].first>>pos[i].second;
    int parity = (abs(pos[0].first)+abs(pos[0].second)) % 2;
    REP(i,N){
        int par2 = (abs(pos[i].first)+abs(pos[i].second)) % 2;
        //45 degree回転する
        pos[i] = pll(pos[i].first + pos[i].second, pos[i].first - pos[i].second);
        if(par2 != parity){
            cout<<-1<<endl;
            return 0;
        }   
    }
    vector<long long>d;
    for(int i = 30; i>=0;i--) d.push_back(1LL<<i);//1<di<10^12
    if(parity%2==0) d.push_back(1);
    cout<<d.size()<<endl;
    REP(j,d.size()) cout<<d[j]<<" ";
    cout<<endl;

    REP(i,N){
        int xdir,ydir;
        ll xsum = 0, ysum = 0;
        FOR(j,0,d.size()){
            if (xsum <= pos[i].first) xdir = 1, xsum += d[j];
            else xdir = -1, xsum -= d[j];

            if(ysum <= pos[i].second) ydir = 1,ysum += d[j];
            else ydir = -1, ysum -= d[j];

            if(xdir == 1 and ydir == 1) cout<<"R";
            else if (xdir == 1 and ydir == -1) cout<<"U";
            else if (xdir == -1 and ydir == -1) cout<<"L";
            else cout<<"D";
        }
        cout<<endl;
    }
}