#include<bits/stdc++.h>
#include "wall.h"
using namespace std;
using ll = int;
#define N 1200003
class SegmentTree {
const ll inf = 1e18;
int n, n0;
ll max_v[4*N], smax_v[4*N], max_c[4*N];
ll min_v[4*N], smin_v[4*N], min_c[4*N];
ll sum[4*N];
ll ecnt[4*N], ladd[4*N];
void update_node_max(int k, ll x) {
sum[k] += (x - max_v[k]) * max_c[k];
if(max_v[k] == min_v[k]) {
max_v[k] = min_v[k] = x;
} else if(max_v[k] == smin_v[k]) {
max_v[k] = smin_v[k] = x;
} else {
max_v[k] = x;
}
}
void update_node_min(int k, ll x) {
sum[k] += (x - min_v[k]) * min_c[k];
if(max_v[k] == min_v[k]) {
max_v[k] = min_v[k] = x;
} else if(smax_v[k] == min_v[k]) {
min_v[k] = smax_v[k] = x;
} else {
min_v[k] = x;
}
}
void push(int k) {
if(ladd[k]) {
addall(2*k+1, ladd[k]);
addall(2*k+2, ladd[k]);
ladd[k] = 0;
}
if(max_v[k] < max_v[2*k+1]) {
update_node_max(2*k+1, max_v[k]);
}
if(min_v[2*k+1] < min_v[k]) {
update_node_min(2*k+1, min_v[k]);
}
if(max_v[k] < max_v[2*k+2]) {
update_node_max(2*k+2, max_v[k]);
}
if(min_v[2*k+2] < min_v[k]) {
update_node_min(2*k+2, min_v[k]);
}
}
void update(int k) {
sum[k] = sum[2*k+1] + sum[2*k+2];
if(max_v[2*k+1] < max_v[2*k+2]) {
max_v[k] = max_v[2*k+2];
max_c[k] = max_c[2*k+2];
smax_v[k] = max(max_v[2*k+1], smax_v[2*k+2]);
} else if(max_v[2*k+1] > max_v[2*k+2]) {
max_v[k] = max_v[2*k+1];
max_c[k] = max_c[2*k+1];
smax_v[k] = max(smax_v[2*k+1], max_v[2*k+2]);
} else {
max_v[k] = max_v[2*k+1];
max_c[k] = max_c[2*k+1] + max_c[2*k+2];
smax_v[k] = max(smax_v[2*k+1], smax_v[2*k+2]);
}
if(min_v[2*k+1] < min_v[2*k+2]) {
min_v[k] = min_v[2*k+1];
min_c[k] = min_c[2*k+1];
smin_v[k] = min(smin_v[2*k+1], min_v[2*k+2]);
} else if(min_v[2*k+1] > min_v[2*k+2]) {
min_v[k] = min_v[2*k+2];
min_c[k] = min_c[2*k+2];
smin_v[k] = min(min_v[2*k+1], smin_v[2*k+2]);
} else {
min_v[k] = min_v[2*k+1];
min_c[k] = min_c[2*k+1] + min_c[2*k+2];
smin_v[k] = min(smin_v[2*k+1], smin_v[2*k+2]);
}
}
void _update_min(ll x, int a, int b, int k, int l, int r) {
if(b <= l || r <= a || max_v[k] <= x) {
return;
}
if(a <= l && r <= b && smax_v[k] < x) {
update_node_max(k, x);
return;
}
push(k);
_update_min(x, a, b, 2*k+1, l, (l+r)/2);
_update_min(x, a, b, 2*k+2, (l+r)/2, r);
update(k);
}
void _update_max(ll x, int a, int b, int k, int l, int r) {
if(b <= l || r <= a || x <= min_v[k]) {
return;
}
if(a <= l && r <= b && x < smin_v[k]) {
update_node_min(k, x);
return;
}
push(k);
_update_max(x, a, b, 2*k+1, l, (l+r)/2);
_update_max(x, a, b, 2*k+2, (l+r)/2, r);
update(k);
}
void addall(int k, ll x) {
max_v[k] += x; smax_v[k] += x;
min_v[k] += x; smin_v[k] += x;
sum[k] += ecnt[k] * x;
ladd[k] += x;
}
void _add(ll x, int a, int b, int k, int l, int r) {
if(b <= l || r <= a) {
return;
}
if(a <= l && r <= b) {
addall(k, x);
return;
}
push(k);
_add(x, a, b, 2*k+1, l, (l+r)/2);
_add(x, a, b, 2*k+2, (l+r)/2, r);
update(k);
}
ll _query_max(int a, int b, int k, int l, int r) {
if(b <= l || r <= a) {
return -inf;
}
if(a <= l && r <= b) {
return max_v[k];
}
push(k);
ll lv = _query_max(a, b, 2*k+1, l, (l+r)/2);
ll rv = _query_max(a, b, 2*k+2, (l+r)/2, r);
return max(lv, rv);
}
ll _query_min(int a, int b, int k, int l, int r) {
if(b <= l || r <= a) {
return inf;
}
if(a <= l && r <= b) {
return min_v[k];
}
push(k);
ll lv = _query_min(a, b, 2*k+1, l, (l+r)/2);
ll rv = _query_min(a, b, 2*k+2, (l+r)/2, r);
return min(lv, rv);
}
ll _query_sum(int a, int b, int k, int l, int r) {
if(b <= l || r <= a) {
return 0;
}
if(a <= l && r <= b) {
return sum[k];
}
push(k);
ll lv = _query_sum(a, b, 2*k+1, l, (l+r)/2);
ll rv = _query_sum(a, b, 2*k+2, (l+r)/2, r);
return lv + rv;
}
public:
SegmentTree(int n) {
SegmentTree(n, nullptr);
}
SegmentTree(int n, ll *a) : n(n) {
n0 = 1;
while(n0 < n) n0 <<= 1;
if(a != nullptr) {
for(int i=0; i<n; ++i) {
max_v[n0-1+i] = min_v[n0-1+i] = sum[n0-1+i] = a[i];
smax_v[n0-1+i] = -inf;
smin_v[n0-1+i] = inf;
max_c[n0-1+i] = min_c[n0-1+i] = 1;
ecnt[n0-1+i] = 1; ladd[n0-1+i] = 0;
}
} else {
for(int i=n; i<n0; ++i) {
max_v[n0-1+i] = min_v[n0-1+i] = sum[n0-1+i] = 0;
smax_v[n0-1+i] = -inf;
smin_v[n0-1+i] = inf;
max_c[n0-1+i] = min_c[n0-1+i] = 1;
ecnt[n0-1+i] = 1; ladd[n0-1+i] = 0;
}
}
for(int i=n; i<n0; ++i) {
max_v[n0-1+i] = smax_v[n0-1+i] = 0;
min_v[n0-1+i] = smin_v[n0-1+i] = 0;
max_c[n0-1+i] = min_c[n0-1+i] = 0;
ecnt[n0-1+i] = ladd[n0-1+i] = 0;
}
for(int i=n0-2; i>=0; i--) {
update(i);
ecnt[i] = ecnt[2*i+1] + ecnt[2*i+2];
}
}
void update_min(int a, int b, ll x) {
_update_min(x, a, b, 0, 0, n0);
}
void update_max(int a, int b, ll x) {
_update_max(x, a, b, 0, 0, n0);
}
void add(int a, int b, ll x) {
_add(x, a, b, 0, 0, n0);
}
ll query_max(int a, int b) {
return _query_max(a, b, 0, 0, n0);
}
ll query_min(int a, int b) {
return _query_min(a, b, 0, 0, n0);
}
ll query_sum(int a, int b) {
return _query_sum(a, b, 0, 0, n0);
}
};
ll v[N];
void buildWall(int n, int k, int op[], int left[], int right[], int height[], int finalHeight[]){
SegmentTree stb(n+1, v);
for(int i=0;i<k;i++){
if(op[i]==1){
stb.update_max(left[i],right[i]+1,height[i]);
}else{
stb.update_min(left[i],right[i]+1,height[i]);
}
}
for(int i=0;i<n;i++){
finalHeight[i]=stb.query_max(i,i+1);
}
/*
10 3
1 3 4 91220
1 5 9 48623
2 3 5 39412*/
/*int a, b;
ll x, r0, r1;
int c = 0;
while(++c) {
a = gen(mt); b = gen(mt);
if(a == b) continue;
if(a > b) swap(a, b);
switch(rtype(mt)) {
case 0:
x = val(mt);
stb.update_min(a, b, x);
for(int i=a; i<b; ++i) {
if(x < v[i]) v[i] = x;
}
break;
case 1:
x = val(mt);
stb.update_max(a, b, x);
for(int i=a; i<b; ++i) {
if(v[i] < x) v[i] = x;
}
break;
case 2:
r0 = stb.query_max(a, b);
r1 = 0;
for(int i=a; i<b; ++i) {
if(r1 < v[i]) r1 = v[i];
}
break;
case 3:
r0 = stb.query_min(a, b);
r1 = (1e18);
for(int i=a; i<b; ++i) {
if(v[i] < r1) r1 = v[i];
}
break;
case 4:
r0 = stb.query_sum(a, b);
r1 = 0;
for(int i=a; i<b; ++i) {
r1 += v[i];
}
break;
case 5:
stb.add(a, b, x);
for(int i=a; i<b; ++i) {
v[i] += x;
}
break;
}
}*/
}
