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;

#define rep(i, a, b) for (ll i = (a); i < (b); i++)
typedef uint64_t ull;
typedef int64_t ll;
typedef std::pair<ll, ll> PLL;

signed main() {
    ll N;
    cin>>N;
    vector<ll> X(N), Y(N);
    bool even=false, odd=false;
    rep (i,0,N) {
        cin>>X[i]>>Y[i];
        if (abs(X[i]+Y[i])%2 == 0) {
            even=true;
        } else {
            odd=true;
        }
    }
    if (odd && even) {
        cout<<-1<<endl;
        return 0;
    }
    vector<ll> d;
    for (ll i=31; i>=0; i--) {
        d.push_back(1ll << i);
    }
    if (even) {
        d.push_back(1);
    }

    cout<<d.size()<<endl;
    for (auto e : d) {
        cout<<e<<endl;
    }

    rep(i,0,N){
        string ans="";
        for (auto e: d){
            if (abs(X[i]) > abs(Y[i])) {
                if (X[i] > 0) {
                    // Right
                    ans += "R";
                    X[i] -= e;
                } else {
                    // Left
                    ans += "L";
                    X[i] += e;
                }
            } else {
                if (Y[i] > 0) {
                    // Up
                    ans += "U";
                    Y[i] -= e;
                } else {
                    // Down
                    ans += "D";
                    Y[i] += e;
                }
            }
        }
        cout<<ans<<endl;
    }
    return 0;
}