/*
このコード、と～おれ!
Be accepted!
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		  　　　　　　　　　　(¸.·´ (¸.·'* ☆
*/

#include <cstdio>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstring>
#include <vector>
#include <numeric>
#include <iostream>
#include <random>
#include <map>
#include <unordered_map>
#include <queue>
#include <regex>
#include <functional>
#include <complex>
#include <list>
#include <cassert>
#include <iomanip>
#include <set>
#include <stack>
#include <bitset>

////多倍長整数, cpp_intで宣言
//#include <boost/multiprecision/cpp_int.hpp>
//using namespace boost::multiprecision;

//#pragma gcc target ("avx2")
//#pragma gcc optimization ("Ofast")
//#pragma gcc optimization ("unroll-loops")
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define rep1(i, n) for(int i = 1; i <= (n); ++i)
#define rep2(i, n) for(int i = 2; i < (n); ++i)
#define repr(i, n) for(int i = n; i >= 0; --i)
#define reprm(i, n) for(int i = n - 1; i >= 0; --i)
#define printynl(a) printf(a ? "yes\n" : "no\n")
#define printyn(a) printf(a ? "Yes\n" : "No\n")
#define printYN(a) printf(a ? "YES\n" : "NO\n")
#define printim(a) printf(a ? "possible\n" : "imposible\n")
#define printdb(a) printf("%.50lf\n", a) //少数出力
#define printLdb(a) printf("%.50Lf\n", a) //少数出力
#define printdbd(a) printf("%.16lf\n", a) //少数出力(桁少なめ)
#define prints(s) printf("%s\n", s.c_str()) //string出力
#define all(x) (x).begin(), (x).end()
#define deg_to_rad(deg) (((deg)/360.0L)*2.0L*PI)
#define rad_to_deg(rad) (((rad)/2.0L/PI)*360.0L)
#define Please return
#define AC 0
#define manhattan_dist(a, b, c, d) (abs(a - c) + abs(b - d)) /*(a, b) から (c, d) のマンハッタン距離 */
#define inf numeric_limits<double>::infinity();
#define linf numeric_limits<long double>::infinity()

using ll = long long;
using ull = unsigned long long;

constexpr int INF = 1073741823;
constexpr int MINF = -1073741823;
constexpr ll LINF = ll(4661686018427387903);
constexpr ll MOD = 1e9 + 7;
constexpr long double eps = 1e-6;
const long double PI = acosl(-1.0L);

using namespace std;

void scans(string & str) {
	char c;
	str = "";
	scanf("%c", &c);
	if (c == '\n')scanf("%c", &c);
	while (c != '\n' && c != -1 && c != ' ') {
		str += c;
		scanf("%c", &c);
	}
}

void scanc(char& str) {
	char c;
	scanf("%c", &c);
	if (c == -1)return;
	while (c == '\n') {
		scanf("%c", &c);
	}
	str = c;
}

double acot(double x) {
	return PI / 2 - atan(x);
}

ll LSB(ll n) { return (n & (-n)); }

/*-----------------------------------------ここからコード-----------------------------------------*/



int main() {

	int q, n;
	scanf("%d%d%*c", &q, &n);
	vector<vector<int>> p(n / 2, vector<int>(n / 2));
	vector<string> s(n);
	rep(i, n) {
		rep(j, n) {
			int h = i, w = j;
			if (h >= n / 2)h = n - h - 1;
			if (w >= n / 2)w = n - w - 1;
			char c;
			scanf("%c", &c);
			if (c == '1')++p[h][w];
			s[i] += c;
		}
		scanf("%*c");
	}
	set<pair<int, int>> ng;
	rep(i, n / 2) {
		rep(j, n / 2) {
			if (p[i][j] % 4)ng.insert({ i, j });
		}
	}
	int ans = ng.empty();
	while (--q) {
		int d;
		scanf("%d", &d);
		if (d == 0) {
			ans += ng.empty();
			continue;
		}
		while (d--) {
			int r, c;
			scanf("%d%d", &r, &c);
			--r, --c;
			if (s[r][c] == '1') {
				s[r][c] = '0';
				if (r >= n / 2)r = n - r - 1;
				if (c >= n / 2)c = n - c - 1;
				--p[r][c];
				if (p[r][c] % 4 == 0)ng.erase({ r, c });
				else if (p[r][c] == 3)ng.insert({ r, c });
			}
			else if (s[r][c] == '0') {
				s[r][c] = '1';
				if (r >= n / 2)r = n - r - 1;
				if (c >= n / 2)c = n - c - 1;
				++p[r][c];
				if (p[r][c] % 4 == 0)ng.erase({ r, c });
				else if (p[r][c] == 1)ng.insert({ r, c });
			}
		}
		ans += ng.empty();
	}
	printf("%d\n", ans);

	Please AC;
}


Measured memory_bytes: 13836