## Editorial for Bảng ô vuông

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

#### Code mẫu của happyboy99x

#include<algorithm>
#include<climits>
#include<cstdio>
#include<cstring>
using namespace std;

#define MAX 14
#define FOR(i, a, b) for(int i = (a), _b = (b); i <= _b; ++i)

int r, a[MAX+2][MAX+2], t[MAX+2][MAX+2];

void touch(int i, int j, int & cnt) {
++cnt;
t[i][j] = 1 - t[i][j];
t[i-1][j] = 1 - t[i-1][j];
t[i+1][j] = 1 - t[i+1][j];
t[i][j-1] = 1 - t[i][j-1];
t[i][j+1] = 1 - t[i][j+1];
}

bool white() {
FOR(i, 1, r) if(t[r][i]) return 0;
return 1;
}

void solve() {
int res = INT_MAX;
FOR(fst, 0, (1 << r) - 1) {
memcpy(t, a, sizeof a); int cnt = 0;
FOR(i, 0, r-1) if(fst & (1 << i)) touch(1, i+1, cnt);
FOR(i, 2, r) FOR(j, 1, r) if(t[i-1][j]) touch(i, j, cnt);
if(white()) res = min(res, cnt);
}
FOR(i,1,r) FOR(j,1,r) a[i][j] = 1 - a[i][j];
FOR(fst, 0, (1 << r) - 1) {
memcpy(t, a, sizeof a); int cnt = 0;
FOR(i, 0, r-1) if(fst & (1 << i)) touch(1, i+1, cnt);
FOR(i, 2, r) FOR(j, 1, r) if(t[i-1][j]) touch(i, j, cnt);
if(white()) res = min(res, cnt);
}
printf("%d\n", res == INT_MAX ? -1 : res);
}

void enter() {
scanf("%d",&r); char s[MAX+2];
FOR(i, 1, r) {
scanf("%s", s+1);
FOR(j, 1, r) a[i][j] = s[j] - 0x30;
}
}

int main() {
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
#endif
enter();
solve();
return 0;
}


program c11touch;
uses    math;
const   fi='';
maxN=16;
var     a,d:array[0..maxN,0..maxN] of longint;
n,res,target:longint;

procedure input;
var     f:text;
i,j:longint;
c:char;
begin
assign(f,fi);
reset(f);
for i:=1 to n do
begin
for j:=1 to n do
begin
a[i,j]:=ord(c)-48;
end;
end;
close(f);
end;

procedure update(k:longint);
var     i:longint;
begin
for i:=1 to n do
if d[n,i]<>target then exit;
res:=k;
end;

procedure back(i,j,k:longint);
begin
if k>=res then exit;
if i>n then
begin
update(k);
exit;
end;
if i=1 then
begin
if j<n then back(i,j+1,k)
else back(i+1,1,k);
d[i-1,j]:=d[i-1,j] xor 1;
d[i,j]:=d[i,j] xor 1;
d[i,j-1]:=d[i,j-1] xor 1;
d[i,j+1]:=d[i,j+1] xor 1;
d[i+1,j]:=d[i+1,j] xor 1;
if j<n then back(i,j+1,k+1)
else back(i+1,1,k+1);
d[i-1,j]:=d[i-1,j] xor 1;
d[i,j]:=d[i,j] xor 1;
d[i,j-1]:=d[i,j-1] xor 1;
d[i,j+1]:=d[i,j+1] xor 1;
d[i+1,j]:=d[i+1,j] xor 1;
end
else
begin
if d[i-1,j]=target then
if j<n then back(i,j+1,k)
else back(i+1,1,k)
else
begin
d[i-1,j]:=d[i-1,j] xor 1;
d[i,j]:=d[i,j] xor 1;
d[i,j-1]:=d[i,j-1] xor 1;
d[i,j+1]:=d[i,j+1] xor 1;
d[i+1,j]:=d[i+1,j] xor 1;
if j<n then back(i,j+1,k+1)
else back(i+1,1,k+1);
d[i-1,j]:=d[i-1,j] xor 1;
d[i,j]:=d[i,j] xor 1;
d[i,j-1]:=d[i,j-1] xor 1;
d[i,j+1]:=d[i,j+1] xor 1;
d[i+1,j]:=d[i+1,j] xor 1;
end;
end;
end;

procedure process;
begin
res:=maxLongint;
d:=a;
target:=0;
back(1,1,0);
d:=a;
target:=1;
back(1,1,0);
if res=maxLongint
then res:=-1;
end;

begin
input;
process;
write(res);
end.


#### Code mẫu của RR

#include <sstream>
#include <iomanip>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <string>
#include <deque>
#include <complex>

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define FORN(i,a,b) for(int i=(a),_b=(b);i<_b;i++)
#define DOWN(i,a,b) for(int i=a,_b=(b);i>=_b;i--)
#define SET(a,v) memset(a,v,sizeof(a))
#define sqr(x) ((x)*(x))
#define ll long long
#define F first
#define S second
#define PB push_back
#define MP make_pair

#define DEBUG(x) cout << #x << " = "; cout << x << endl;
#define PR(a,n) cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl;
#define PR0(a,n) cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl;
using namespace std;

int INP,AM,REACHEOF;
#define BUFSIZE (1<<12)
char BUF[BUFSIZE+1], *inp=BUF;
#define GETCHAR(INP) { \
if(!*inp) { \
if (REACHEOF) return 0;\
memset(BUF,0,sizeof BUF);\
if (inpzzz != BUFSIZE) REACHEOF = true;\
inp=BUF; \
} \
INP=*inp++; \
}
#define DIG(a) (((a)>='0')&&((a)<='9'))
#define GN(j) { \
AM=0;\
GETCHAR(INP); while(!DIG(INP) && INP!='-') GETCHAR(INP);\
if (INP=='-') {AM=1;GETCHAR(INP);} \
j=INP-'0'; GETCHAR(INP); \
while(DIG(INP)){j=10*j+(INP-'0');GETCHAR(INP);} \
if (AM) j=-j;\
}

const long double PI = acos((long double) -1.0);

#define TWO(x) (1<<(x))
#define CONTAIN(S,x) (S & TWO(x))
;

int n, res, now;
char a[111][111];
int c[111];

inline void flip(int i, int j) {
++now;
if (i) c[i-1] ^= TWO(j);
if (i+1 < n) c[i+1] ^= TWO(j);
c[i] ^= TWO(j);
if (j) c[i] ^= TWO(j-1);
if (j+1 < n) c[i] ^= TWO(j+1);
}

void update(int s) {
REP(i,n) {
c[i] = 0;
REP(j,n)
if (a[i][j] == '1') c[i] |= TWO(j);
}

now = 0;
REP(j,n) if (CONTAIN(s,j)) {
flip(0,j);
}

FOR(i,1,n-1) REP(j,n)
if (CONTAIN(c[i-1], j)) {
flip(i, j);
}
if (c[n-1]) return ;
res = min(res, now);
}

int main() {
scanf("%d\n", &n);
REP(i,n) gets(a[i]);

res = n*n+1;

REP(turn,2) {
REP(s,TWO(n)) update(s);

REP(i,n) REP(j,n)
if (a[i][j] == '1') a[i][j] = '0';
else a[i][j] = '1';
}
if (res > n*n) res = -1;
printf("%d\n", res);
return 0;
}


#### Code mẫu của hieult

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <iomanip>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef unsigned int ui;
typedef unsigned long long ull;

#define Rep(i,n) for(__typeof(n) i = 0; i < (n); ++i)
#define Repd(i,n) for(__typeof(n) i = (n)-1; i >= 0; --i)
#define For(i,a,b) for(__typeof(b) i = (a); i <= (b); ++i)
#define Ford(i,a,b) for(__typeof(a) i = (a); i >= (b); --i)
#define Fit(i,v) for(__typeof((v).begin()) i = (v).begin(); i != (v).end(); ++i)
#define Fitd(i,v) for(__typeof((v).rbegin()) i = (v).rbegin(); i != (v).rend(); ++i)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define sz(a) ((int)(a).size())
#define all(a) (a).begin(), (a).end()
#define ms(a,x) memset(a, x, sizeof(a))
#define nl puts("")
#define sp printf(" ")
#define ok puts("ok")
//#include <conio.h>

template<class F, class T> T convert(F a, int p = -1) { stringstream ss; if (p >= 0) ss << fixed << setprecision(p); ss << a; T r; ss >> r; return r; }
template<class T> void db(T a, int p = -1) { if (p >= 0) cout << fixed << setprecision(p); cout << a << " "; }
template<class T> T gcd(T a, T b) { T r; while (b != 0) { r = a % b; a = b; b = r; } return a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
template<class T> T sqr(T x) { return x * x; }
template<class T> T cube(T x) { return x * x * x; }
template<class T> struct Triple { T x, y, z; Triple() {} Triple(T _x, T _y, T _z) : x(_x), y(_y), z(_z) {} };
template<class T> Triple<T> euclid(T a, T b) { if (b == 0) return Triple<T>(1, 0, a); Triple<T> r = euclid(b, a % b); return Triple<T>(r.y, r.x - a / b * r.y, r.z); }
template<class T> int getbit(T s, int i) { return (s >> i) & 1; }
template<class T> T onbit(T s, int i) { return s | (T(1) << i); }
template<class T> T offbit(T s, int i) { return s & (~(T(1) << i)); }
template<class T> int cntbit(T s) { return s == 0 ? 0 : cntbit(s >> 1) + (s & 1); }
const int bfsz = 1 << 16; char bf[bfsz + 5]; int rsz = 0;int ptr = 0;
char gc() { if (rsz <= 0) { ptr = 0; rsz = fread(bf, 1, bfsz, stdin); if (rsz <= 0) return EOF; } --rsz; return bf[ptr++]; }
void ga(char &c) { c = EOF; while (!isalpha(c)) c = gc(); }
int gs(char s[]) { int l = 0; char c = gc(); while (isspace(c)) c = gc(); while (c != EOF && !isspace(c)) { s[l++] = c; c = gc(); } s[l] = '\0'; return l; }
template<class T> bool gi(T &v) {
v = 0; char c = gc(); while (c != EOF && c != '-' && !isdigit(c)) c = gc(); if (c == EOF) return false; bool neg = c == '-'; if (neg) c = gc();
while (isdigit(c)) { v = v * 10 + c - '0'; c = gc(); } if (neg) v = -v; return true;
}

const double PI = 2 * acos(0);
const string months[] = {"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"};
const int days[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int dr[] = {0, 0, 0, -1, +1};
const int dc[] = {0, -1, +1, 0, 0};
const int inf = (int)1e9 + 5;
const ll linf = (ll)1e16 + 5;
const double eps = ld(1e-12);
const ll mod = 1000000000;
typedef pair<int, int> II;

#define maxn 100005

using namespace std;

int n;
string s[20];
int x[20][20], a[15][15];

bool thoaman(int r, int c){
return (r >= 0 && r < n && c >= 0 && c < n);
}

int cal(int r, int c){
int rr, cc, res = 0;
Rep(t, 5){
rr = r + dr[t]; cc = c + dc[t];
if(thoaman(rr, cc)) res += a[rr][cc];
}
return res & 1;
}

ms(a, 0);
Rep(i, n) if(getbit(mask, i)) a[0][i] = 1;
Rep(i, n - 1) Rep(j, n){
a[i + 1][j] = cal(i, j) ^ x[i][j];
res += a[i + 1][j];
}

Rep(i, n) if(cal(n - 1, i) ^ x[n - 1][i]) return inf;
return res;
}

int main(){
//    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
scanf("%d", &n);
Rep(i, n){
cin >> s[i];
Rep(j, n) x[i][j] = s[i][j] - '0';
}

int res = inf;
Rep(run, 1 << n){
res = min(res, go(run));
}

Rep(i, n) Rep(j, n) x[i][j] = 1 - x[i][j];
Rep(run, 1 << n){
res = min(res, go(run));
}

if(res < inf) printf("%d", res);
else printf("-1");
// cout << clock() << endl;
return 0;
}


#### Code mẫu của skyvn97

#include<stdio.h>
#define MAX   20
#define INF   100000
int x[MAX][MAX];
char a[MAX][MAX];
int n,m;
void init(void)
{
int i,j;
scanf("%d",&n);
for (i=1;i<=n;i=i+1)
scanf("%s",&a[i]);
for (i=1;i<=n;i=i+1)
for (j=n;j>=1;j=j-1)
{
a[i][j]=a[i][j-1]-48;
x[i][j]=0;
}
m=INF;
}
void change(int x,int y)
{
a[x-1][y]=1-a[x-1][y];
a[x][y-1]=1-a[x][y-1];
a[x+1][y]=1-a[x+1][y];
a[x][y+1]=1-a[x][y+1];
a[x][y]=1-a[x][y];
}
void count(int v)
{
int i,j,c;
bool b;
b=true;
c=0;
for (i=1;i<=n;i=i+1)
if (x[1][i]==1)
{
change(1,i);
c=c+1;
}
for (i=2;i<=n;i=i+1)
for (j=1;j<=n;j=j+1)
if (a[i-1][j]!=v)
{
x[i][j]=1;
change(i,j);
c=c+1;
}
for (i=1;i<=n;i=i+1)
if (a[n][i]!=v)
{
b=false;
break;
}
if ((b) && (c<m)) m=c;
for (i=1;i<=n;i=i+1)
for (j=1;j<=n;j=j+1)
if (x[i][j]==1)
{
if (i>1) x[i][j]=0;
change(i,j);
}
}
void btrk(int k,int v)
{
int i;
for (i=0;i<=1;i=i+1)
{
x[1][k]=i;
if (k==n) count(v);
else btrk(k+1,v);
}
}
void process(void)
{
init();
btrk(1,0);
btrk(1,1);
if (m>=INF) printf("-1");
else printf("%d",m);
}
int main(void)
{
process();
}