Bob is playing a game of Spaceship Solitaire. The goal of this game is to build a spaceship. In order to do this, he first needs to accumulate enough resources for the construction. There are $n$ types of resources, numbered $1$ through $n$. Bob needs at least $a_i$ pieces of the $i$-th resource to build the spaceship. The number $a_i$ is called **the goal for resource $i$**.

Each resource takes $1$ turn to produce and in each turn only one resource can be produced. However, there are certain milestones that speed up production. Every milestone is a triple $(s_j, t_j, u_j)$, meaning that as soon as Bob has $t_j$ units of the resource $s_j$, he receives one unit of the resource $u_j$ for free, without him needing to spend a turn. It is possible that getting this free resource allows Bob to claim reward for another milestone. This way, he can obtain a large number of resources in a single turn.

The game is constructed in such a way that there are never two milestones that have the same $s_j$ **and** $t_j$, that is, the award for reaching $t_j$ units of resource $s_j$ is at most one additional resource.

**A bonus is never awarded for $0$ of any resource, neither for reaching the goal $a_i$ nor for going past the goal — formally, for every milestone $0 < t_j < a_{s_j}$.**

A bonus for reaching certain amount of a resource can be the resource itself, that is, $s_j = u_j$.

Initially there are no milestones. You are to process $q$ updates, each of which adds, removes or modifies a milestone. After every update, output the minimum number of turns needed to finish the game, that is, to accumulate at least $a_i$ of $i$-th resource for each $i \in [1, n]$.Input

The first line contains a single integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the number of types of resources.

The second line contains $n$ space separated integers $a_1, a_2, \dots, a_n$ ($1 \leq a_i \leq 10^9$), the $i$-th of which is the goal for the $i$-th resource.

The third line contains a single integer $q$ ($1 \leq q \leq 10^5$) — the number of updates to the game milestones.

Then $q$ lines follow, the $j$-th of which contains three space separated integers $s_j$, $t_j$, $u_j$ ($1 \leq s_j \leq n$, $1 \leq t_j < a_{s_j}$, $0 \leq u_j \leq n$). For each triple, perform the following actions:

- First, if there is already a milestone for obtaining $t_j$ units of resource $s_j$, it is removed.
- If $u_j = 0$, no new milestone is added.
- If $u_j \neq 0$, add the following milestone: “For reaching $t_j$ units of resource $s_j$, gain one free piece of $u_j$.”
- Output the minimum number of turns needed to win the game.

Output

Output $q$ lines, each consisting of a single integer, the $i$-th represents the answer after the $i$-th update.Exampleinput

2 2 3 5 2 1 1 2 2 1 1 1 1 2 1 2 2 2 0

output

4 3 3 2 3

Note

After the first update, the optimal strategy is as follows. First produce $2$ once, which gives a free resource $1$. Then, produce $2$ twice and $1$ once, for a total of four turns.

After the second update, the optimal strategy is to produce $2$ three times — the first two times a single unit of resource $1$ is also granted.

After the third update, the game is won as follows.

- First produce $2$ once. This gives a free unit of $1$. This gives additional bonus of resource $1$. After the first turn, the number of resources is thus $[2, 1]$.
- Next, produce resource $2$ again, which gives another unit of $1$.
- After this, produce one more unit of $2$.

The final count of resources is $[3, 3]$, and three turns are needed to reach this situation. Notice that we have more of resource $1$ than its goal, which is of no use.

**Solution:**

#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(false); cin.tie(0); int n; cin >> n; vector<int> a(n); for (int i = 0; i < n; i++) { cin >> a[i]; } long long ans = 0; for (int i = 0; i < n; i++) { ans += a[i]; } vector<int> b(n); map<pair<int, int>, int> mp; auto Remove = [&](int s, int t, int u) { ans += min(a[u], b[u]); --b[u]; ans -= min(a[u], b[u]); }; auto Add = [&](int s, int t, int u) { ans += min(a[u], b[u]); ++b[u]; ans -= min(a[u], b[u]); }; int tt; cin >> tt; while (tt--) { int s, t, u; cin >> s >> t >> u; --s; --u; auto p = make_pair(s, t); auto it = mp.find(p); if (it != mp.end()) { int uu = it->second; mp.erase(it); Remove(s, t, uu); } if (u != -1) { mp[p] = u; Add(s, t, u); } cout << ans << '\n'; } return 0; }