CF - C. A Mist of Florescence

There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.

The wood can be represented by a rectangular grid of $n$

rows and $m$

columns. In each cell of the grid, there is exactly one type of flowers.

According to Mino, the numbers of connected components formed by each kind of flowers are $a$

, $b$, $c$ and $d$

respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.

You are to help Kanno depict such a grid of flowers, with $n$

and $m$

arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.

Note that you can choose arbitrary $n$

and $m$

under the constraints below, they are not given in the input.

Input

The first and only line of input contains four space-separated integers $a$

, $b$, $c$ and $d$ ( $1\le a,b,c,d\le 100$

) — the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.

Output

In the first line, output two space-separated integers $n$

and $m$ ( $1\le n,m\le 50$

) — the number of rows and the number of columns in the grid respectively.

Then output $n$

lines each consisting of $m$

consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.

In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).

Examples

Input

Copy

5 3 2 1

Output

Copy

4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD

Input

Copy

50 50 1 1

Output

Copy

4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Input

Copy

1 6 4 5

Output

Copy

7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD

Note

In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.

。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。

本来不会做，后来看了大神的代码，才理解。。。

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string.h>
#include<string>
#include<math.h>
#include<stdlib.h>
#include<queue>
#include<map>
#include<set>
#include<stack>
#define bug printf("*********\n");
#define mem0(a) memset(a, 0, sizeof(a));
#define mem1(a) memset(a, -1, sizeof(a));
#define finf(a, n) fill(a, a+n, INF);
#define in1(a) scanf("%d" ,&a);
#define in2(a, b) scanf("%d%d", &a, &b);
#define in3(a, b, c) scanf("%d%d%d", &a, &b, &c);
#define out1(a) printf("%d\n", a);
#define out2(a, b) printf("%d %d\n", a, b);
#define pb(G, a, b) G[a].push_back(b);
using namespace std;
typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int, int> par;
const int mod = 998244353;
const LL INF = 1e15;
const int N = 1010;
const double pi = 3.1415926;

char mmp[60][60];

void init()
{
    for(int i = 0; i < 25; i ++) {
        for(int j = 0; j < 25; j ++) {
            mmp[i][j] = 'B';
        }
    }
    for(int i = 0; i < 25; i ++) {
        for(int j = 25; j < 50; j ++) {
            mmp[i][j] = 'A';
        }
    }
    for(int i = 25; i < 50; i ++) {
        for(int j = 0; j < 25; j ++) {
            mmp[i][j] = 'D';
        }
    }
    for(int i = 25; i < 50; i ++) {
        for(int j = 25; j < 50; j ++) {
            mmp[i][j] = 'C';
        }
    }
}

int main()
{
    init();
    int a, b, c, d;
    scanf("%d%d%d%d", &a, &b, &c, &d);
    a -= 1;
    b -= 1;
    c -= 1;
    d -= 1;
    for(int i = 0; i < 25&&a; i ++) {
        for(int j = 0; j < 25&&a; j ++) {
            if(i%2 && j%2) {
                mmp[i][j] = 'A';
                a --;
            }
        }
    }
    for(int i = 0; i < 25&&b; i ++) {
        for(int j = 25; j < 50&&b; j ++) {
            if(i%2 == 0 && j%2 == 0) {
                mmp[i][j] = 'B';
                b --;
            }
        }
    }
    for(int i = 25; i < 50&&c; i ++) {
        for(int j = 0; j < 25&&c; j ++) {
            if(i%2 && j%2) {
                mmp[i][j] = 'C';
                c --;
            }
        }
    }
    for(int i = 25; i < 50&&d; i ++) {  
        for(int j = 25; j < 50&&d; j ++) {
            if(i%2 == 0 && j%2 == 0) {
                mmp[i][j] = 'D';
                d --;
            }
        }
    }
    printf("50 50\n");
    for(int i = 0; i < 50;  i++) {
        for(int j = 0; j < 50; j ++) {
            printf("%c", mmp[i][j]);
        }
        printf("\n");
    }
    return 0;
}

m妙啊。