14457.cpp

/*
 * Scroll down to see solution ty :)
 */
#pragma region template
#pragma clang diagnostic ignored "-Wno-deprecated"
#pragma clang diagnostic ignored "-Werror"
/*
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
*/
// whitecard.cpp : This file contains the 'main' function. Program execution begins and ends there.
#include <bits/stdc++.h>
using namespace std; //名前空間の宣言
using std::cout; using std::cin;
using std::endl; using std::string;
using std::vector; using std::istringstream;
using std::ios;
using std::stringstream;
using std::chrono::duration_cast;
using namespace std::chrono;
using ll = long long; using ld = long double;
using ull = unsigned long long; using str = string;
using bl = bool; using ch = char;
using cd = complex<ld>;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef set<ll> sl;
typedef unordered_set<ll> usl;
typedef unordered_set<str> uss;
typedef vector<vector<ll>> vl2;
typedef vector<str> vs;
typedef vector<ch> vc;
typedef vector<pair<ll, ll>> vp;
typedef vector<bl> vb;
typedef map<ll, str> mls;
typedef map<str, str> mss;
typedef map<ll, ll> mll;
typedef map<str, ll> msl;
typedef map<ch, ll> mcl;
typedef map<ld, ld> mdd;
typedef queue<ll> ql;
typedef deque<ll> dql;
typedef priority_queue<ll> pql;
#define _USE_MATH_DEFINES
#define M_PI 3.14159265358979323846
#define LL_MAX 9223372036854775807
#define ScanfNowTryToBeatMyCompileSpeed std::ios::sync_with_stdio(EXIT_SUCCESS); std::cin.tie(EXIT_SUCCESS); std::cout.tie(EXIT_SUCCESS);
#define up(initial, n, step) for(ll i = (ll)(initial);i < (ll)(n);i+=(ll)(step))
#define up2(initial, n, step) for(ll j = (ll)(initial);j < (ll)(n);j+=(ll)(step))
#define up3(initial, n, step) for(ll k = (ll)(initial);k < (ll)(n);k+=(ll)(step))
#define down(initial, n, step) for(ll i = (ll)(initial) - 1;i >= (ll)(n);i-=(ll)(step))
#define all(x) (x).begin(), (x).end()
#define vget(v) for(auto& element : v) element = get();
#define vcin(v) for(auto& element : v) cin >> (element);
#define YES(a) ((a)?"YES":"NO")
#define Yes(a) ((a)?"Yes":"No")
#define yes(a) ((a)?"yes":"no")
#define stop return EXIT_SUCCESS;
#define rev(s) reverse((s).begin(), (s).end());
#define sortCol(v, v2, col) sort(v, v[(col)] < v2[(col)])
#define vsort(v) sort(v.begin(), v.end())
#define vsum(v) accumulate(v.begin(), v.end(), 0)
#define vprint(v, spacing) foreach(x, v)cout << (x) << (spacing)
#define toStr(s) to_string((s))
#define throwErr(s) throw invalid_argument(s)
#define setdecimal(n) cout << fixed << setprecision((n))
#define fillAsc(v, start) iota((v).begin(), (v).end(), (start))
#define nextPerm next_permutation
#define prevPerm prev_permutation
#define varConcat(a, b) a##b
#define foreach(a, v) for(auto& a : v)
#define skip continue
#define stc static
#define _m_ int main(void)
#define tc \
  ll testcase = get();  \
  while (testcase--)
#define tcin \
  ll testcase;\
  cin >> testcase;\
  while(testcase--)
auto _ = NULL;//Shame that C++ does not have Discards like C#.
const str alphabet = "abcdefghijklmnopqrstuvwxyz";
const str upAlphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const ld PHI = (1 + sqrt(5)) / 2;
const ll Mod = 998244353;
const ll Mod2 = pow(10, 9) + 7;
const ld EPS = 1e-9;
const ld PI = 2 * acos(0.0);
str toLower(str s) { str result = ""; for (auto& c : s)result += tolower(c); return result; }
str toUpper(str s) { str result = ""; for (auto& c : s)result += toupper(c); return result; }
ld TAN(ld degree) { return tan(degree * PI / 180.0); };
ld SIN(ld degree) { return sin(degree * PI / 180.0); };
ld COS(ld degree) { return cos(degree * PI / 180.0); };
ld ATAN(ld len) { return atan(len) * 180 / PI; }
ld ASIN(ld len) { return asin(len) * 180 / PI; }
ld ACOS(ld len) { return acos(len) * 180 / PI; }
ll lexOrder(str s, str s1) { if (s == s1) stop; if (s.length() <= s1.length()) { up(0, s.length(), 1) { if (s[i] < s1[i]) return -1; else if (s[i] > s1[i]) return 1; } return -1; } else { for (int i = 0; i < s1.length(); i++) { if (s[i] > s1[i]) return -1; else if (s[i] < s1[i]) return 1; } return 1; } }
ll revBinarySearch(vector<int> v, int X) { int start = 0, end = v.size() - 1; while (start <= end) { int mid = start + (end - start) / 2; if (X == v[mid]) return mid; else if (X < v[mid]) start = mid + 1; else end = mid - 1; } return -1; }
bl isNumber(const str& st) { for (ch const& c : st) if (isdigit(c) == 0) return false; return true; }
ll getMonth(str m) { m = toLower(m); if (m == "january") return 1; else if (m == "february") return 2; else if (m == "march") return 3; else if (m == "april") return 4; else if (m == "may") return 5; else if (m == "june") return 6; else if (m == "july") return 7; else if (m == "august") return 8; else if (m == "sepember") return 9; else if (m == "october") return 10; else if (m == "november") return 11; return 12; }
bl isLeapYear(int n) { return (n % 4 == 0 ? n % 100 == 0 && n % 400 == 0 ? true : n % 100 != 0 ? true : false : false); }
bl sortcol(const vector<int>& v, const vector<int>& v2, int col) { return v[col] < v2[col]; }
bl cmp(pair<str, ll>& a, pair<str, ll>& b) { if (a.second == b.second) { for (ll i = 0; i < min(a.first.length(), b.first.length()); i++) { if (a.first[i] < b.first[i])return 0; else if (a.first[i] > b.first[i])return 1; } } return a.second < b.second; }
ll gcd(ll a, ll b) { while (b) b ^= a ^= b ^= a %= b; return a; }
ll lcm(ll a, ll b) { return (abs(a * b) / gcd(a, b)); }
bl islower(str s) { for (const auto& c : s) { if (c > 'z' || c < 'a') return false; } return true; }
bl isupper(str s) { for (const auto& c : s) { if (c > 'Z' || c < 'A') return false; } return true; }
ll ascSum(ll n) { return n * (n + 1) / 2; }
ll fib(ll num) { const ld f = sqrt(5); return (pow(1 + f, num) - pow(1 - f, num)) / (pow(2, num) * f); }//1,1,2,3,5,8,13,21,34,55,...
ll vColSum(vl2 v, ll col) { ll sum = 0; foreach(x, v) sum += x[col]; return sum; }
ll mapMaxElement(mll x) { mll::iterator best = max_element(x.begin(), x.end(), [](const pair<ll, ll>& a, const pair<ll, ll>& b)->bool { return a.second < b.second; }); return best->second; }
ll mapMaxElement(msl x) { msl::iterator best = max_element(x.begin(), x.end(), [](const pair<str, ll>& a, const pair<str, ll>& b)->bool { return a.second < b.second; }); return best->second; }
bl isPrime(ll n) { if (n == 1) return 0; for (ll i = 2; i * i <= n; i++) if (!(n % i))return 0; return 1; }
vl eratosthenesSieve(ll limit) { vl prime(limit + 1); for (ll i = 2; i <= limit; i++)prime[i] = 1; for (ll p = 2; p * p <= limit; p++)if (prime[p])for (ll i = p * p; i <= limit; i += p)prime[i] = 0; return prime; }
vl linearSieve(ll limit) { vl lp(limit + 1), pr; up(2, limit + 1, 1) { if (!lp[i]) lp[i] = i, pr.push_back(i); for (ll j = 0; i * pr[j] <= limit; ++j) { lp[i * pr[j]] = pr[j]; if (pr[j] == lp[i]) break; } } return pr; }
bl isPow2(ll i) { return i && (i & -i) == i; }
bl isPal(str s) { str s1 = s; rev(s1); return s1 == s; }
bl isParenthesis(str s) { ll p = 0; foreach(t, s) { if (t == '(')p++; else if (t == ')') { p--; if (p < 0)  return false; } }return p == 0; }
vl factor(ll n) { vl v; up(1, sqrt(n) + 1, 1) if (!(n % i)) { v.push_back(i); v.push_back(n / i); } return v; }
ull fa(ull n) { ull i, fa = 1; for (i = n; i > 1; i--) fa *= i; return fa; }
ull nCr(ull n, ull r) { ull nume = 1, i; for (i = n; i > r; i--) nume *= i; return ull(nume / fa(n - r)); }
ll bigmod(ll a, ll b, ll m) { ll res = 1 % m; while (b) { if (b & 1) res = (res * a) % m; a = (a * a) % m, b >>= 1; }return res; }
auto vmin = [](vl v) {return *min_element(all(v)); };
auto vmax = [](vl v) {return *max_element(all(v)); };
auto multiply = [](ll n, ll n2, ll m = 1) {ll result = 0; while (n2 > 0) { if (n2 & 1)  result += n; n = n << 1; n2 = n2 >> 1; result %= m; } return result; };
ull faM(ull n, ull m) { ull i, fa = 1; for (i = n; i > 1; i--) fa = multiply(fa, i, m); return fa; }
ll lis(vl v) { vl s2(v.size(), 0); ll L = 1; s2[0] = v[0]; up(1, v.size(), 1) { auto it = lower_bound(s2.begin(), s2.begin() + L, v[i]); if (it == s2.begin() + L) s2[L++] = v[i]; else *it = v[i]; }return L; }
vl primeFactors(ll n) { vl res; while (!(n % 2)) res.push_back(2), n /= 2; for (ll i = 3; i * i <= n; i += 2) while (!(n % i)) res.push_back(i), n /= i; if (n > 2) res.push_back(n); return res; }
ll longest_common_subsequence(string X, string Y, ll m, ll n) { vl2 L(m, vl(n)); for (int i = 0; i <= m; i++) { for (int j = 0; j <= n; j++) { if (i == 0 || j == 0) L[i][j] = 0; else if (X[i - 1] == Y[j - 1]) L[i][j] = L[i - 1][j - 1] + 1; else L[i][j] = max(L[i - 1][j], L[i][j - 1]); } } return L[m][n]; }
ll MEX(vl A) { sl b(A.begin(), A.end()); ll result = 0; while (b.count(result)) ++result; return result; }
//Unity Engine based Vector2
class Vector2 {
public:
    ld x, y;
    friend Vector2 operator-(const Vector2&, const Vector2&);
};
Vector2 operator-(const Vector2& a, const Vector2& b) {
    Vector2 v;
    v.x = a.x - b.x, v.y - a.y - b.y;
    return v;
}
ld Distance(Vector2& a, Vector2& b) {
    return sqrtl(powl(a.x - b.x, 2) + powl(a.y - b.y, 2));
}
ld magnitude(Vector2* a) {
    return sqrtl(powl(a->x, 2) + powl(a->y, 2));
}
ld manhattanDistance(Vector2& a, Vector2& b) {
    return fabsl(a.x - b.x) + fabsl(a.y - b.y);
}
bl collinear(Vector2 a, Vector2 b, Vector2 c) {
    return (b.y - a.y) * (c.x - b.x) == (c.y - b.y) * (b.x - a.x);
}
//fastInput, fastOutput and BigInt provided by GeeksForGeeks
inline ll get(void) { ch t = getchar(); ll x = 0, neg = 0; while ((t < 48 || t>57) && t != '-') t = getchar(); if (t == '-') { neg = 1; t = getchar(); } while (t >= 48 && t <= 57) { x = (x << 3) + (x << 1) + t - 48; t = getchar(); } if (neg) x = -x; return x; }
inline void out(ll x, ll mode = 1) { ch a[20]; a[0] = '0'; ll i = 0, j; if (x < 0) { putchar('-'); x = -x; }if (x == 0) putchar('0'); while (x) { a[i++] = x % 10 + 48; x /= 10; } for (j = i - 1; j >= 0; j--) putchar(a[j]); putchar(mode ? '\n' : ' '); }
//fastPow provided by rookiesLab
ull fastPow(ull b, ull power) {
    ull result = 1;
    while (power > 0) {
        if (power % 2 == 1) result = (result * b);
        b = (b * b);
        power /= 2;
    }
    return result;
}
ull fastPowMod(ull b, ull power, ull mod) {
    b %= mod;
    ull result = 1;
    while (power > 0) {
        if (power % 2 == 1) result = (result * b) % mod;
        b = (b * b) % mod;
        power /= 2;
    }
    return result;
}
bl isInt(ld n) { return n - (ll)n <= EPS; }
template <typename T>
class fenwick {
public:
    vector<T> fenw;
    int n;

    fenwick(int _n) : n(_n) {
        fenw.resize(n);
    }

    void modify(int x, T v) {
        while (x < n) {
            fenw[x] += v;
            x |= (x + 1);
        }
    }

    T get(int x) {
        T v{};
        while (x >= 0) {
            v += fenw[x];
            x = (x & (x + 1)) - 1;
        }
        return v;
    }
};
struct FenwickTree2D {
    vector<vector<int>> bit;
    vector<int>g;
    int n, m;
    void init(int n, int m) {
        this->n = n;
        this->m = m;
        for (int i = 0; i < n; i++)
        {
            g.assign(m, 0);
            bit.push_back(g);
        }
    }
    FenwickTree2D(int n, int m, vector<vector<int>>a) {
        init(n, m);
        for (size_t i = 0; i < a.size(); i++)
            for (size_t j = 0; j < a[i].size(); j++)
                add(i, j, a[i][j]);
    }
    int sum(int x, int y) {
        int ret = 0;
        for (int i = x; i >= 0; i = (i & (i + 1)) - 1)
            for (int j = y; j >= 0; j = (j & (j + 1)) - 1)
                ret += bit[i][j];
        return ret;
    }

    void add(int x, int y, int delta) {
        for (int i = x; i < n; i = i | (i + 1))
            for (int j = y; j < m; j = j | (j + 1))
                bit[i][j] += delta;
    }
};
ll reverse(ll num, ll lg_n) {
    ll res = 0;
    up(0, lg_n, 1) if (num & (1 << i)) res |= 1 << (lg_n - 1 - i);
    return res;
}
void FFT(vector<cd>& a, bl invert) {
    ll n = a.size(), lg_n = 0;
    while ((1 << lg_n) < n) lg_n++;
    for (ll i = 0; i < n; i++) if (i < reverse(i, lg_n)) swap(a[i], a[reverse(i, lg_n)]);
    for (ll len = 2; len <= n; len <<= 1) {
        ld ang = 2 * PI / len * (invert ? -1 : 1);
        cd wlen(cos(ang), sin(ang));
        for (int i = 0; i < n; i += len) {
            cd w(1);
            for (ll j = 0; j < len / 2; j++) {
                cd u = a[i + j], v = a[i + j + len / 2] * w;
                a[i + j] = u + v;
                a[i + j + len / 2] = u - v;
                w *= wlen;
            }
        }
    }
    if (invert) for (cd& x : a) x /= n;
}
struct segmentTree {
    //change segmentTree for different problem.
    ll SIZE;
    vl sums;
    void init(ll n) { //init for given size
        SIZE = 1;
        while (SIZE < n) SIZE *= 2;
        sums.assign(2 * SIZE, 0LL);
    }
    void init(vl& v, ll x, ll lx, ll rx) {
        if (rx - lx == 1) {
            if (lx < (ll)v.size()) sums[x] = v[lx];
            return;
        }
        ll m = (lx + rx) / 2;
        init(v, 2 * x + 1, lx, m);
        init(v, 2 * x + 2, m, rx);
        sums[x] = sums[2 * x + 1] + sums[2 * x + 2];
        return;
    }
    void init(vl& v) { //init for given array
        init(v, 0, 0, SIZE);
    }
    void set(ll i, ll v, ll x, ll l, ll r) { //add to segment below. x is the index in the tree
        if (r - l == 1) {
            sums[x] = v;
            return;
        }
        ll m = (l + r) / 2;
        if (i < m) set(i, v, 2 * x + 1, l, m);
        else set(i, v, 2 * x + 2, m, r);
        sums[x] = sums[2 * x + 1] + sums[2 * x + 2];
        return;
    }
    void set(ll i, ll v) { //assign 0-indexed i to value v
        set(i, v, 0, 0, SIZE);
    }
    ll sum(ll l, ll r, ll x, ll lx, ll rx) {
        if (lx >= r || l >= rx) return 0;
        if (lx >= l && rx <= r) return sums[x];
        ll m = (lx + rx) / 2;
        return sum(l, r, 2 * x + 1, lx, m) + sum(l, r, 2 * x + 2, m, rx);
    }
    ll sum(ll l, ll r) { //from l to r - 1 inclusively
        return sum(l, r, 0, 0, SIZE);
    }
};
vb r;  // removed
vl s;   // subtree size
vl2 tree, centroidTree;
ll centroid_dfs(ll n, ll p = 0) {
    s[n] = 1;
    for (ll x : tree[n])
        if (x != p && !r[x]) s[n] += centroid_dfs(x, n);
    return s[n];
}
ll get_centroid(ll n, ll ms, ll p = 0)  // n = node, ms = size of tree, p = parent
{
    for (int x : tree[n])
        if (x != p && !r[x])
            if (s[x] * 2 > ms) return get_centroid(x, ms, n);
    return n;
}
ll centroid_(ll n = 1) {
    ll C = get_centroid(n, centroid_dfs(n));
    r[C] = 1;
    for (ll x : tree[C])
        if (!r[x]) {
            ll sub = centroid_(x);
            centroidTree[sub].push_back(C), centroidTree[C].push_back(sub);
        }
    return C;
}
ll centroid(ll SIZE) {
    r.resize(SIZE);
    s.resize(SIZE);
    centroidTree.resize(SIZE);
    return centroid_(1);
}
void setIO(string s) {
    freopen((s + ".in").c_str(), "r", stdin);
    freopen((s + ".out").c_str(), "w", stdout);
}
ll inter_area(vl s1, vl s2) {
    ll bl_a_x = s1[0], bl_a_y = s1[1], tr_a_x = s1[2], tr_a_y = s1[3];
    ll bl_b_x = s2[0], bl_b_y = s2[1], tr_b_x = s2[2], tr_b_y = s2[3];

    return ((min(tr_a_x, tr_b_x) - max(bl_a_x, bl_b_x)) *
        (min(tr_a_y, tr_b_y) - max(bl_a_y, bl_b_y)));
}
bool covered(int x, int y, int x1, int y1, int x2, int y2) {
    return x >= x1 && x <= x2 && y >= y1 && y <= y2;
}
#pragma endregion
_m_{ //main関数の開始
ScanfNowTryToBeatMyCompileSpeed
//setIO("cowtip");
ll n; cin >> n;
vs v(n);
vcin(v);
ll cnt = 0;
set<pair<ll, ll>> s;
s.insert({ n - 1, n - 1 });
while (s.size()) {
    set<pair<ll, ll>> temp;
    foreach(x, s) {
        ll i = x.first, j = x.second;
        if (v[i][j] == '1') {
            for (ll k = 0; k <= i; k++) for (ll m = 0; m <= j; m++) v[k][m] = v[k][m] == '0' ? '1' : '0';
            cnt++;
        }
        if (i - 1 >= 0) temp.insert({ i - 1, j });
        if (j - 1 >= 0) temp.insert({ i, j - 1 });
    }
    s = temp;
}
cout << cnt << '\n';
stop //プログラムを終了
}