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(int i=0;i<(n);++i)
using namespace std;
using ll = long long;
using cand_t = pair<char,pair<ll,ll>>;
ll d_l1(pair<ll,ll> a,pair<ll,ll> b){
    return abs(a.first-b.first)+abs(a.second-b.second);
}
void arm(pair<ll,ll> p_start,pair<ll,ll> p_end,ll dist){
    if(dist==0&&p_start==p_end){
        cout << endl;
        return;
    }
    if(dist<1)dist=1;
    vector<cand_t> candidate;
    candidate.push_back({'L',{p_start.first-dist,p_start.second}});
    candidate.push_back({'R',{p_start.first+dist,p_start.second}});
    candidate.push_back({'D',{p_start.first,p_start.second-dist}});
    candidate.push_back({'U',{p_start.first,p_start.second+dist}});
    std::sort(candidate.begin(),candidate.end(),[&](cand_t a,cand_t b){return d_l1(p_end,a.second)<d_l1(p_end,b.second);});
    cout << candidate[0].first;
    arm(candidate[0].second,p_end,dist/2);
}
int main(){
    int n;
    cin >> n;
    vector<pair<ll,ll>> xy;
    bool is_even;
    rep(i,n){
        ll x,y;
        cin >> x >> y;
        if(i==0)is_even=((x+y)%2==0);
        else if(is_even!=((x+y)%2==0)){
            cout << -1 << endl;
            return 0;
        }
        xy.push_back({x,y});
    }
    cout << 33 + (is_even?1:0) << endl;
    rep(i,33) cout << (1LL<<(32-i)) << " ";
    if(is_even) cout << 1;
    cout << endl;
    rep(i,n)arm({0,0},xy[i],1LL<<32);
    return 0;
}