#include <bits/stdc++.h>
using namespace std;
#define f(i,a,b) for(int i=int(a);i<int(b);++i)
#define vt vector
#define pb push_back
template<class A> void rd(vt<A>& v);
template<class T> void rd(T& x){ cin >> x; }
template<class H, class... T> void rd(H& h, T&... t) { rd(h) ; rd(t...) ;}
template<class A> void rd(vt<A>& x) { for(auto& a : x) rd(a) ;}
/*
* description :- polynomial hashing of strings.
* sources :- https://codeforces.com/contest/710/submission/102996468
* verification :- https://codeforces.com/contest/154/submission/120344887
*/
#ifdef int
static_assert(false,"do not define int");
#endif
template<const unsigned &MOD>
struct _m_uint {
unsigned val;
_m_uint(int64_t v = 0) {
if(v < 0) v = v % MOD + MOD;
if(v >= MOD) v %= MOD;
val = unsigned(v);
}
_m_uint(uint64_t v) {
if(v >= MOD) v %= MOD;
val = unsigned(v);
}
_m_uint(int v) : _m_uint(int64_t(v)) {}
_m_uint(unsigned v) : _m_uint(uint64_t(v)) {}
explicit operator unsigned() const { return val; }
explicit operator int64_t() const { return val; }
explicit operator uint64_t() const { return val; }
explicit operator double() const { return val; }
explicit operator long double() const { return val; }
_m_uint& operator+=(const _m_uint &other) {
val = val < MOD - other.val ? val + other.val : val - (MOD - other.val);
return *this;
}
_m_uint& operator-=(const _m_uint &other) {
val = val < other.val ? val + (MOD - other.val) : val - other.val;
return *this;
}
static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
#if !defined(_WIN32) || defined(_WIN64)
return unsigned(x % m);
#endif
// Optimized mod for Codeforces 32-bit machines.
// x must be less than 2^32 * m for this to work, so that x / m fits in an unsigned 32-bit int.
unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
unsigned quot, rem;
asm("divl %4\n"
: "=a" (quot), "=d" (rem)
: "d" (x_high), "a" (x_low), "r" (m));
return rem;
}
_m_uint& operator*=(const _m_uint &other) {
val = fast_mod(uint64_t(val) * other.val);
return *this;
}
_m_uint& operator/=(const _m_uint &other) {
return *this *= other.inv();
}
friend _m_uint operator+(const _m_uint &a, const _m_uint &b) { return _m_uint(a) += b; }
friend _m_uint operator-(const _m_uint &a, const _m_uint &b) { return _m_uint(a) -= b; }
friend _m_uint operator*(const _m_uint &a, const _m_uint &b) { return _m_uint(a) *= b; }
friend _m_uint operator/(const _m_uint &a, const _m_uint &b) { return _m_uint(a) /= b; }
_m_uint& operator++() {
val = val == MOD - 1 ? 0 : val + 1;
return *this;
}
_m_uint& operator--() {
val = val == 0 ? MOD - 1 : val - 1;
return *this;
}
_m_uint operator++(int) { _m_uint before = *this; ++*this; return before; }
_m_uint operator--(int) { _m_uint before = *this; --*this; return before; }
_m_uint operator-() const {
return val == 0 ? 0 : MOD - val;
}
friend bool operator==(const _m_uint &a, const _m_uint &b) { return a.val == b.val; }
friend bool operator!=(const _m_uint &a, const _m_uint &b) { return a.val != b.val; }
friend bool operator<(const _m_uint &a, const _m_uint &b) { return a.val < b.val; }
friend bool operator>(const _m_uint &a, const _m_uint &b) { return a.val > b.val; }
friend bool operator<=(const _m_uint &a, const _m_uint &b) { return a.val <= b.val; }
friend bool operator>=(const _m_uint &a, const _m_uint &b) { return a.val >= b.val; }
static const int SAVE_INV = int(1e6) + 5;
static _m_uint save_inv[SAVE_INV];
static void prepare_inv() {
// Make sure MOD is prime, which is necessary for the inverse algorithm below.
for(int64_t p = 2; p * p <= MOD; p += p % 2 + 1){
assert(MOD % p != 0);
}
save_inv[0] = 0;
save_inv[1] = 1;
for (int i = 2; i < SAVE_INV; i++){
save_inv[i] = save_inv[MOD % i] * (MOD - MOD / i);
}
}
_m_uint inv() const {
if(save_inv[1] == 0) prepare_inv();
if(val < SAVE_INV) return save_inv[val];
_m_uint product = 1;
unsigned v = val;
while (v >= SAVE_INV) {
product *= MOD - MOD / v;
v = MOD % v;
}
return product * save_inv[v];
}
_m_uint pow(int64_t p) const {
if (p < 0) return inv().pow(-p);
_m_uint a = *this, result = 1;
while(p > 0) {
if(p & 1) result *= a;
p >>= 1;
if(p > 0) a *= a;
}
return result;
}
friend ostream& operator<<(ostream &os, const _m_uint &m) {
return os << m.val;
}
};
template<const unsigned &MOD> _m_uint<MOD> _m_uint<MOD>::save_inv[_m_uint<MOD>::SAVE_INV];
auto random_address = [] { char *p = new char; delete p; return uint64_t(p); };
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count() * (random_address() | 1));
// P = 2^32 - 13337 is a safe prime: both P and (P - 1) / 2 are prime.
extern const unsigned HASH_P = unsigned(-13337); // hash prime
using hash_int = _m_uint<HASH_P>;
using hash_t = uint64_t;
const uint64_t HASH_P2 = uint64_t(HASH_P) * HASH_P;// square of hash prime
const int HASH_COUNT = 2;
// Avoid multiplication bases near 0 or P - 1.
uniform_int_distribution<unsigned> MULT_DIST(unsigned(0.1 * HASH_P), unsigned(0.9 * HASH_P));
const hash_int HASH_MULT[] = {MULT_DIST(rng), MULT_DIST(rng)}; // our bases
const hash_int HASH_INV[] = {1 / HASH_MULT[0], 1 / HASH_MULT[1]};
vector<hash_int> hash_pow[] = {{1}, {1}};
const int INF = int(1e9) + 5;
template<typename T_string = string>
struct string_hash {
static const bool BUILD_REVERSE = false;
static uint64_t hash(const T_string &str) {
uint64_t result = 0;
for(int h = 0; h < HASH_COUNT; h++) {
uint64_t value = 1;
for(const auto &x : str){
value = (uint64_t(HASH_MULT[h]) * value + x) % HASH_P;
}
result += value << (32 * h);
}
return result;
}
T_string str;
vector<hash_int> _prefix[HASH_COUNT];
vector<hash_int> _inv_prefix[HASH_COUNT];
string_hash() {
build({});
}
string_hash(const T_string &_str) {
build(_str);
}
int length() const {
return int(_prefix[0].size()) - 1;
}
template<typename T_char>
void add_char(const T_char &c) {
str.push_back(c);
for(int h = 0; h < HASH_COUNT; h++) {
_prefix[h].push_back(HASH_MULT[h] * _prefix[h].back() + c);
if(hash_pow[h].size() < _prefix[h].size()){
hash_pow[h].push_back(HASH_MULT[h] * hash_pow[h].back());
}
if(BUILD_REVERSE){
_inv_prefix[h].push_back((_inv_prefix[h].back() + c) * HASH_INV[h]);
}
}
}
void pop_char() {
str.pop_back();
for(int h = 0; h < HASH_COUNT; h++) {
_prefix[h].pop_back();
if(BUILD_REVERSE) {
_inv_prefix[h].pop_back();
}
}
}
void build(const T_string &_str) {
str = {};
str.reserve(_str.size());
for(int h = 0; h < HASH_COUNT; h++) {
hash_pow[h].reserve(_str.size() + 1);
_prefix[h] = {0};
_prefix[h].reserve(_str.size() + 1);
if(BUILD_REVERSE) {
_inv_prefix[h] = {0};
_inv_prefix[h].reserve(_str.size() + 1);
}
}
for(auto &c : _str) add_char(c);
}
uint64_t _single_hash(int h, int start, int end) const {
// Convert everything to `uint64_t` for speed. Note: we add hash_pow[length] to fix strings that start with 0.
uint64_t power = uint64_t(hash_pow[h][end - start]);
return (power + uint64_t(_prefix[h][end]) + HASH_P2 - uint64_t(_prefix[h][start]) * power) % HASH_P;
}
uint64_t substring_hash(int start, int end) const {
assert(0 <= start && start <= end && end <= length());
return _single_hash(0, start, end) + (HASH_COUNT > 1 ? _single_hash(1, start, end) << 32 : 0);
}
uint64_t complete_hash() const {
return substring_hash(0, length());
}
uint64_t _reverse_single_hash(int h, int start, int end) const {
// Convert everything to `uint64_t` for speed. Note: we add hash_pow[length] to fix strings that start with 0.
uint64_t power = uint64_t(hash_pow[h][end - start]);
return (power + uint64_t(_inv_prefix[h][end]) * power + HASH_P - uint64_t(_inv_prefix[h][start])) % HASH_P;
}
uint64_t reverse_substring_hash(int start, int end) const {
assert(0 <= start && start <= end && end <= length());
return _reverse_single_hash(0, start, end) + (HASH_COUNT > 1 ? _reverse_single_hash(1, start, end) << 32 : 0);
}
uint64_t reverse_complete_hash() const {
return reverse_substring_hash(0, length());
}
bool equal(int start1, int start2, int length) const {
return substring_hash(start1, start1 + length) == substring_hash(start2, start2 + length);
}
bool is_palindrome(int start, int end) const {
return substring_hash(start, end) == reverse_substring_hash(start, end);
}
int compare(int start1, int start2, int max_length = INF) const;
};
uint64_t concat_hashes(uint64_t hash1, uint64_t hash2, int len2) {
uint64_t hash1_low = hash1 & unsigned(-1);
uint64_t hash2_low = hash2 & unsigned(-1);
uint64_t power = uint64_t(hash_pow[0][len2]);
uint64_t combined = (hash1_low * power + hash2_low + HASH_P - power) % HASH_P;
if (HASH_COUNT > 1) {
hash1 >>= 32;
hash2 >>= 32;
power = uint64_t(hash_pow[1][len2]);
combined += (hash1 * power + hash2 + HASH_P - power) % HASH_P << 32;
}
return combined;
}
template<typename T_string>
int first_mismatch(const string_hash<T_string> &hash1, int start1,
const string_hash<T_string> &hash2, int start2, int max_length = INF) {
max_length = min({max_length, hash1.length() - start1, hash2.length() - start2});
static const int FIRST = 5;
int first = min(max_length, FIRST);
for(int i = 0; i < first; i++){
if(hash1.str[start1 + i] != hash2.str[start2 + i]){
return i;
}
}
if(hash1.substring_hash(start1, start1 + max_length) == hash2.substring_hash(start2, start2 + max_length)){
return max_length;
}
static const int MANUAL = 15;
int low = first, high = max_length - 1;
while(high - low > MANUAL) {
int mid = (low + high + 1) / 2;
if(hash1.substring_hash(start1, start1 + mid) == hash2.substring_hash(start2, start2 + mid)){
low = mid;
}else{
high = mid - 1;
}
}
for(int i = low; i < high; i++) {
if(hash1.str[start1 + i] != hash2.str[start2 + i]){
return i;
}
}
return high;
}
template<typename T_string>
int hash_compare(const string_hash<T_string> &hash1, int start1,
const string_hash<T_string> &hash2, int start2, int max_length = INF) {
int mismatch = first_mismatch(hash1, start1, hash2, start2, max_length);
int length1 = min(hash1.length() - start1, max_length);
int length2 = min(hash2.length() - start2, max_length);
if(mismatch == min(length1, length2)){
return length1 == length2 ? 0 : (length1 < length2 ? -1 : +1);
}
if(hash1.str[start1 + mismatch] == hash2.str[start2 + mismatch]){
return 0;
}
return hash1.str[start1 + mismatch] < hash2.str[start2 + mismatch] ? -1 : +1;
}
template<typename T_string>
int string_hash<T_string>::compare(int start1, int start2, int max_length) const {
return hash_compare(*this, start1, *this, start2, max_length);
}
template<class T> struct compress_1d_co_ordinates {
vector<T> values;
void add(T x){
values.push_back(x);
return;
}
void gen(){
sort(values.begin(),values.end());
values.erase(unique(values.begin(),values.end()),values.end());
return;
}
int get(T x){
int j = lower_bound(values.begin(),values.end(),x) - values.begin();
assert(values[j] == x); return j;
}
void clear(){
values.clear();
return;
}
};
signed main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int n,m; rd(n,m);
vector<string> s(n);
rd(s);
string_hash<string> string_h[2*n];
f(i,0,n){
string_h[i].build(s[i]+s[i]);
string_h[i+n].build(s[i]+s[i]);
}
vt<int> best(m);
// rotote horizontally
for(int i = 0; i < m; ++i){
vt<hash_t> _strings(2*n);
vt<int> strings;
compress_1d_co_ordinates<hash_t> compress;
for(int j = 0; j < n; ++j){
_strings[j] = _strings[n+j] = string_h[j].substring_hash(i,i+m);
compress.add(_strings[j]);
}
compress.gen();
for(auto& i : _strings) strings.pb(compress.get(i));
compress.clear();
string_hash<vector<int>> vector_h;
vector_h.build(strings);
int current_best = 0;
for(int j = 1; j < n; ++j){
int k = first_mismatch(vector_h,current_best,vector_h,j,n);
if(k == n) continue;
int c = hash_compare(string_h[current_best+k],i,string_h[j+k],i,m);
assert(c != 0);
// if string 2 is small.
if(c == 1) current_best = j;
}
best[i] = current_best;
}
int x = 0;
for(int i = 1; i < m; ++i){
for(int j = 0; j < n; ++j){
if(string_h[best[x] + j].substring_hash(x,x+m) != string_h[best[i] + j].substring_hash(i,i+m)){
int c = hash_compare(string_h[best[x] + j],x,string_h[best[i] + j],i,m);
assert(c != 0);
// if string 2 is small
if(c == 1) x = i;
break;
}
}
}
f(i,0,n){
f(j,0,m){
cout << s[(i+best[x])%n][(j+x)%m];
}
cout << "\n";
}
}
