#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
istream &operator>>(istream &is, i128 &x) {
i64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, i128 x) {
os << (i64) x;
return os;
}
istream &operator>>(istream &is, u128 &x) {
u64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, u128 x) {
os << (u64) x;
return os;
}
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
// ============
#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif
// ============
#include <limits>
#include <utility>
template <typename T>
struct Add {
using Value = T;
static Value id() {
return T(0);
}
static Value op(const Value &lhs, const Value &rhs) {
return lhs + rhs;
}
static Value inv(const Value &x) {
return -x;
}
};
template <typename T>
struct Mul {
using Value = T;
static Value id() {
return Value(1);
}
static Value op(const Value &lhs, const Value &rhs) {
return lhs * rhs;
}
static Value inv(const Value &x) {
return Value(1) / x;
}
};
template <typename T>
struct Min {
using Value = T;
static Value id() {
return std::numeric_limits<T>::max();
}
static Value op(const Value &lhs, const Value &rhs) {
return std::min(lhs, rhs);
}
};
template <typename T>
struct Max {
using Value = T;
static Value id() {
return std::numeric_limits<Value>::min();
}
static Value op(const Value &lhs, const Value &rhs) {
return std::max(lhs, rhs);
}
};
template <typename T>
struct Xor {
using Value = T;
static Value id() {
return T(0);
}
static Value op(const Value &lhs, const Value &rhs) {
return lhs ^ rhs;
}
static Value inv(const Value &x) {
return x;
}
};
template <typename Monoid>
struct Reversible {
using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;
static Value id() {
return Value(Monoid::id(), Monoid::id());
}
static Value op(const Value &v1, const Value &v2) {
return Value(
Monoid::op(v1.first, v2.first),
Monoid::op(v2.second, v1.second));
}
};
// ============
// ============
#include <cassert>
template <typename Monoid>
class SparseSegmentTree {
public:
using Value = typename Monoid::Value;
using Index = long long;
private:
struct Node {
Node *lft;
Node *rgt;
Value prod;
Node(Value v) : lft(nullptr), rgt(nullptr), prod(v) {}
#ifdef LOCAL
~Node() {
if (lft) {
delete lft;
}
if (rgt) {
delete rgt;
}
}
#endif
void update_prod() {
if (!lft && !rgt) {
prod = Monoid::id();
} else if (!lft) {
prod = rgt->prod;
} else if (!rgt) {
prod = lft->prod;
} else {
prod = Monoid::op(lft->prod, rgt->prod);
}
}
};
static Node *update(Node *cur, Index curl, Index curr, Index upd, Value v) {
if (!cur) {
cur = new Node(Monoid::id());
}
if (curr - curl == 1) {
cur->prod = v;
} else {
Index curm = (curl + curr) / 2;
if (upd < curm) {
cur->lft = update(cur->lft, curl, curm, upd, v);
} else {
cur->rgt = update(cur->rgt, curm, curr, upd, v);
}
cur->update_prod();
}
return cur;
}
static Value prod(Node *cur, Index curl, Index curr, Index qryl, Index qryr) {
if (!cur || curr <= qryl || qryr <= curl) {
return Monoid::id();
}
if (qryl <= curl && curr <= qryr) {
return cur->prod;
}
Index curm = (curl + curr) / 2;
Value pl = prod(cur->lft, curl, curm, qryl, qryr);
Value pr = prod(cur->rgt, curm, curr, qryl, qryr);
return Monoid::op(pl, pr);
}
Index lft;
Index rgt;
Node *root;
public:
SparseSegmentTree() : lft(0), rgt(1), root(nullptr) {}
SparseSegmentTree(Index n) : lft(0), rgt(n), root(nullptr) {
assert(n > 0);
}
SparseSegmentTree(Index l, Index r) : lft(l), rgt(r), root(nullptr) {
assert(l < r);
}
void update(Index idx, Value v) {
root = update(root, lft, rgt, idx, v);
}
Value prod(Index l, Index r) const {
return prod(root, lft, rgt, l, r);
}
};
// ============
// ============
#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>
class HeavyLightDecomposition {
std::vector<int> siz;
std::vector<int> par;
std::vector<int> hea;
std::vector<int> in;
std::vector<int> out;
std::vector<int> dep;
std::vector<int> rev;
template <typename G>
void dfs1(G &g, int v) {
if (!g[v].empty() && (int) g[v][0] == par[v]) {
std::swap(g[v][0], g[v].back());
}
for (auto &e : g[v]) {
int u = (int)e;
if (u != par[v]) {
par[u] = v;
dfs1(g, u);
siz[v] += siz[u];
if (siz[u] > siz[(int) g[v][0]]) {
std::swap(g[v][0], e);
}
}
}
}
template <typename G>
void dfs2(const G &g, int v, int &time) {
in[v] = time;
rev[time++] = v;
for (auto &e : g[v]) {
int u = (int)e;
if (u == par[v]) {
continue;
}
if (u == (int) g[v][0]) {
hea[u] = hea[v];
} else {
hea[u] = u;
}
dep[u] = dep[v] + 1;
dfs2(g, u, time);
}
out[v] = time;
}
public:
template <typename G>
HeavyLightDecomposition(G &g, int root = 0) :
siz(g.size(), 1),
par(g.size(), root),
hea(g.size(), root),
in(g.size(), 0),
out(g.size(), 0),
dep(g.size(), 0),
rev(g.size(), 0) {
assert(root >= 0 && root < (int) g.size());
dfs1(g, root);
int time = 0;
dfs2(g, root, time);
}
int subtree_size(int v) const {
assert(v >= 0 && v < (int) siz.size());
return siz[v];
}
int parent(int v) const {
assert(v >= 0 && v < (int) par.size());
return par[v];
}
int in_time(int v) const {
assert(v >= 0 && v < (int) in.size());
return in[v];
}
int out_time(int v) const {
assert(v >= 0 && v < (int) out.size());
return out[v];
}
int depth(int v) const {
assert(v >= 0 && v < (int) dep.size());
return dep[v];
}
int time_to_vertex(int t) const {
assert(t >= 0 && t < (int) rev.size());
return rev[t];
}
int la(int v, int k) const {
assert(v >= 0 && v < (int) dep.size());
assert(k >= 0);
if (k > dep[v]) {
return -1;
}
while (true) {
int u = hea[v];
if (in[u] + k <= in[v]) {
return rev[in[v] - k];
}
k -= in[v] - in[u] + 1;
v = par[u];
}
return 0;
}
int forward(int v, int dst) const {
assert(v >= 0 && v < (int) dep.size());
assert(dst >= 0 && dst < (int) dep.size());
assert(v != dst);
int l = lca(v, dst);
if (l == v) {
return la(dst, dist(v, dst) - 1);
} else {
return par[v];
}
}
int lca(int u, int v) const {
assert(u >= 0 && u < (int) dep.size());
assert(v >= 0 && v < (int) dep.size());
while (u != v) {
if (in[u] > in[v]) {
std::swap(u, v);
}
if (hea[u] == hea[v]) {
v = u;
} else {
v = par[hea[v]];
}
}
return u;
}
int dist(int u, int v) const {
assert(u >= 0 && u < (int) dep.size());
assert(v >= 0 && v < (int) dep.size());
return dep[u] + dep[v] - 2 * dep[lca(u, v)];
}
std::vector<std::pair<int, int>> path(int u, int v, bool edge) const {
assert(u >= 0 && u < (int) dep.size());
assert(v >= 0 && v < (int) dep.size());
std::vector<std::pair<int, int>> fromu, fromv;
bool rev = false;
while (true) {
if (u == v && edge) {
break;
}
if (in[u] > in[v]) {
std::swap(u, v);
std::swap(fromu, fromv);
rev ^= true;
}
if (hea[u] == hea[v]) {
fromv.emplace_back(in[v], in[u] + (int)edge);
v = u;
break;
} else {
fromv.emplace_back(in[v], in[hea[v]]);
v = par[hea[v]];
}
}
if (rev) {
std::swap(fromu, fromv);
}
std::reverse(fromv.begin(), fromv.end());
fromu.reserve(fromv.size());
for (auto [x, y] : fromv) {
fromu.emplace_back(y, x);
}
return fromu;
}
int jump(int u, int v, int k) const {
assert(u >= 0 && u < (int) dep.size());
assert(v >= 0 && v < (int) dep.size());
assert(k >= 0);
int l = lca(u, v);
int dis = dep[u] + dep[v] - 2 * dep[l];
if (k > dis) {
return -1;
}
if (k <= dep[u] - dep[l]) {
return la(u, k);
} else {
return la(v, dis - k);
}
}
int meet(int u, int v, int w) const {
return lca(u, v) ^ lca(v, w) ^ lca(w, u);
}
};
// ============
struct Converted {
i32 n;
Vec<Vec<i32>> tree;
i32 rt;
Vec<i32> a;
i32 q;
Vec<tuple<i32, i32, i32>> queries; // (0, v, x) or (1, v, -1) or (1, n, -1)
};
Converted convert(i32 r, i32 c, i32 q, const Vec<Vec<i32>> &l,
const Vec<Vec<i32>> &p,
const Vec<tuple<i32, i32, i32, i32>> &queries) {
Vec<i32> par(r * c, -1);
auto find_root = [&](const auto &find_root, i32 v) -> i32 {
if (par[v] == -1) {
return v;
} else {
return par[v] = find_root(find_root, par[v]);
}
};
Vec<pair<i32, i32>> events;
REP(i, q) {
auto [ty, x, y, val] = queries[i];
if (ty == 1) {
events.emplace_back(val, r * c + i);
}
}
REP(i, r) REP(j, c) { events.emplace_back(l[i][j], i * c + j); }
sort(ALL(events));
const i32 dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
Vec<Vec<i32>> tree(r * c);
Vec<tuple<i32, i32, i32>> qs(q, make_tuple(0, 0, 0));
for (auto [_, i] : events) {
if (i < r * c) {
i32 x = i / c;
i32 y = i - x * c;
REP(dir, 4) {
i32 tx = x + dx[dir], ty = y + dy[dir];
if (tx >= 0 && tx < r && ty >= 0 && ty < c &&
l[x][y] > l[tx][ty]) {
i32 tr = find_root(find_root, tx * c + ty);
if (tr != x * c + y) {
par[tr] = x * c + y;
tree[x * c + y].emplace_back(tr);
tree[tr].emplace_back(x * c + y);
}
}
}
} else {
i -= r * c;
auto [_ty, x, y, val] = queries[i];
if (val < l[x][y]) {
qs[i] = make_tuple(1, r * c, -1);
} else {
i32 rt = find_root(find_root, x * c + y);
qs[i] = make_tuple(1, rt, -1);
}
}
}
REP(i, q) {
auto [ty, x, y, val] = queries[i];
if (ty == 0) {
qs[i] = make_tuple(0, x * c + y, val);
}
}
i32 mx_x = -1, mx_y = -1, mx = -1;
REP(i, r) REP(j, c) {
if (chmax(mx, l[i][j])) {
mx_x = i;
mx_y = j;
}
}
Vec<i32> a;
a.reserve(r * c);
REP(i, r) REP(j, c) { a.push_back(p[i][j]); }
return Converted{r * c, tree, mx_x * c + mx_y, a, q, qs};
}
Vec<i32> solve(Converted prob) {
HeavyLightDecomposition hld(prob.tree, prob.rt);
i32 k = 0;
REP(i, prob.n) { chmax(k, prob.a[i]); }
for (auto [ty, x, y] : prob.queries) {
if (ty == 0) {
chmax(k, y);
}
}
++k;
Vec<SparseSegmentTree<Add<i32>>> segs;
segs.reserve(k);
REP(i, k) { segs.emplace_back(SparseSegmentTree<Add<i32>>(prob.n + 1)); }
SparseSegmentTree<Add<i32>> siz(prob.n);
auto add = [&](i32 v, i32 x) -> void {
for (auto [l, r] : hld.path(prob.rt, v, false)) {
++r;
segs[x].update(l, segs[x].prod(l, l + 1) + 1);
segs[x].update(r, segs[x].prod(r, r + 1) - 1);
}
i32 dep = hld.depth(v);
i32 ok = -1, ng = dep + 1;
while (ng - ok > 1) {
i32 mid = (ok + ng) / 2;
i32 u = hld.la(v, mid);
if (segs[x].prod(0, hld.in_time(u) + 1) == 1) {
ok = mid;
} else {
ng = mid;
}
}
if (ok != -1) {
i32 u = hld.la(v, ok);
for (auto [l, r] : hld.path(u, v, false)) {
++r;
siz.update(l, siz.prod(l, l + 1) + 1);
siz.update(r, siz.prod(r, r + 1) - 1);
}
}
};
auto sub = [&](i32 v, i32 x) -> void {
for (auto [l, r] : hld.path(prob.rt, v, false)) {
++r;
segs[x].update(l, segs[x].prod(l, l + 1) - 1);
segs[x].update(r, segs[x].prod(r, r + 1) + 1);
}
i32 dep = hld.depth(v);
i32 ok = -1, ng = dep + 1;
while (ng - ok > 1) {
i32 mid = (ok + ng) / 2;
i32 u = hld.la(v, mid);
if (segs[x].prod(0, hld.in_time(u) + 1) == 0) {
ok = mid;
} else {
ng = mid;
}
}
if (ok != -1) {
i32 u = hld.la(v, ok);
for (auto [l, r] : hld.path(u, v, false)) {
++r;
siz.update(l, siz.prod(l, l + 1) - 1);
siz.update(r, siz.prod(r, r + 1) + 1);
}
}
};
REP(v, prob.n) { add(v, prob.a[v]); }
Vec<i32> ans;
for (auto [ty, x, y] : prob.queries) {
if (ty == 0) {
sub(x, prob.a[x]);
prob.a[x] = y;
add(x, prob.a[x]);
} else {
if (x == prob.n) {
ans.push_back(0);
} else {
x = hld.in_time(x);
ans.push_back(siz.prod(0, x + 1));
}
}
}
return ans;
}
int main() {
i32 r, c, q;
cin >> r >> c >> q;
Vec<Vec<i32>> l(r, Vec<i32>(c));
REP(i, r) REP(j, c) { cin >> l[i][j]; }
Vec<Vec<i32>> p(r, Vec<i32>(c));
REP(i, r) REP(j, c) { cin >> p[i][j]; }
Vec<i32> dis;
dis.reserve(r * c);
REP(i, r) REP(j, c) { dis.push_back(l[i][j]); }
sort(ALL(l));
//REP(i, dis.size() - 1) { assert(dis[i] != dis[i + 1]); }
Vec<tuple<i32, i32, i32, i32>> queries(q);
for (auto &[ty, x, y, val] : queries) {
cin >> ty >> y >> x >> val;
--ty;
--y;
--x;
}
Converted prob = convert(r, c, q, l, p, queries);
Vec<i32> ans = solve(prob);
for (i32 ele : ans) {
cout << ele << '\n';
}
}
