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>
# define R register int
# define ll long long

using namespace std;

const int N=1003;
int n,f0,f1,m;
int x[N],y[N];
ll c[N];

ll ab (ll a)
{
    if(a<0) return -a;
    return a;
}

void write (int x,int y)
{
    printf("\n");
    ll nx=0,ny=0;
    for (R i=1;i<=m;++i)
    {
        if(ab(nx-x)>ab(ny-y))
        {
            if(nx>x) printf("L"),nx-=c[i];
            else printf("R"),nx+=c[i];
        }
        else
        {
            if(ny>y) printf("D"),ny-=c[i];
            else printf("U"),ny+=c[i];
        }
    }
    if(nx!=x||ny!=y) puts("WA"); 
}

int main()
{
    scanf("%d",&n);
    for (R i=1;i<=n;++i)
    {
        scanf("%d%d",&x[i],&y[i]);
        if((x[i]+y[i])%2) f1=1;
        else f0=1;
    }
    if(f0&&f1) { puts("-1"); return 0; }
    if(f0) c[++m]=1;
    for (R i=0;i<=38;++i) c[++m]=1ll<<i;
    printf("%d\n",m);
    for (R i=1;i<=m/2;++i) swap(c[i],c[m-i+1]);
    for (R i=1;i<=m;++i) printf("%lld ",c[i]);
    for (R i=1;i<=n;++i) write(x[i],y[i]);
    return 0;
}