One measure of ``unsortedness'' in a sequence is the number of pairs of entries that are out of order with respect to each other. For instance, in the letter sequence ``DAABEC'', this measure is 5, since D is greater than four letters to its right and E is greater than one letter to its right. This measure is called the number of inversions in the sequence. The sequence ``AACEDGG'' has only one inversion (E and D)---it is nearly sorted---while the sequence ``ZWQM'' has 6 inversions (it is as unsorted as can be---exactly the reverse of sorted).

You are responsible for cataloguing a sequence of DNA strings (sequences containing only the four letters A, C, G, and T). However, you want to catalog them, not in alphabetical order, but rather in order of ``sortedness'', from ``most sorted'' to ``least sorted''. All the strings are of the same length.

The first line contains two integers: a positive integer n (0 < n <= 50) giving the length of the strings; and a positive integer m (0 < m <= 100) giving the number of strings. These are followed by m lines, each containing a string of length n.

Output the list of input strings, arranged from ``most sorted'' to ``least sorted''. Since two strings can be equally sorted, then output them according to the orginal order.

AACATGAAGG

TTTTGGCCAA

TTTGGCCAAA

GATCAGATTT

CCCGGGGGGA

ATCGATGCAT

CCCGGGGGGA

AACATGAAGG

GATCAGATTT

ATCGATGCAT

TTTTGGCCAA

TTTGGCCAAA

#include <iostream>

#include <cstdio>

#include <algorithm>

#include <cmath>

#include <stack>

#include <vector>

#include <queue>

#include <cstring>

#include <string>

#include <map>

#include <set>

using namespace std;

const int BufferSize = 1 << 16;

char buffer[BufferSize], *Head, *Tail;

inline char Getchar() {

    if(Head == Tail) {

        int l = fread(buffer, 1, BufferSize, stdin);

        Tail = (Head = buffer) + l;

    }

    return *Head++;

}

int read() {

    int x = 0, f = 1; char c = getchar();

    while(!isdigit(c)){ if(c == '-') f = -1; c = getchar(); }

    while(isdigit(c)){ x = x * 10 + c - '0'; c = getchar(); }

    return x * f;

}

#define maxn 110

#define maxl 60

int n, l;

char S[maxn][maxl];

vector <int> id[maxn*maxn];

void process(int x) {

	int A = 0, C = 0, G = 0, sum = 0;

	for(int i = l; i >= 1; i--) {

		if(S[x][i] == 'A') A++;

		if(S[x][i] == 'C') sum += A, C++;

		if(S[x][i] == 'G') sum += A + C, G++;

		if(S[x][i] == 'T') sum += A + C + G;

	}

	id[sum].push_back(x);

	return ;

}

int main() {

	l = read(); n = read();

	for(int i = 1; i <= n; i++) scanf("%s", S[i] + 1), process(i);

	for(int i = 0; i <= l * l; i++)

		for(int j = 0; j < id[i].size(); j++) printf("%s\n", S[id[i][j]] + 1);

	return 0;

}