#include <bits/stdc++.h>

using namespace std;

#define MAX_V 514
#define INF 1e9
typedef pair<int, int> pii;

struct Edge {
    int to, cap, cost, rev;
    Edge(int to, int cap, int cost, int rev) :
        to(to), cap(cap), cost(cost), rev(rev) {}
};

int V, h[MAX_V], dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
vector<Edge> G[MAX_V];

void add_edge(int from, int to, int cap, int cost)
{
    G[from].push_back(Edge(to, cap, cost, G[to].size()));
    G[to].push_back(Edge(from, 0, -cost, G[from].size()-1));
}

int min_cost_flow(int s, int t, int f)
{
    int res = 0;
    fill(h, h+V, 0);
    while (f > 0) {
	priority_queue<pii, vector<pii>, greater<pii>> Q;
	fill(dist, dist+V, INF);
	dist[s] = 0;
	Q.push(pii(0, s));
	while (!Q.empty()) {
	    pii p = Q.top(); Q.pop();
	    int v = p.second;
	    if (dist[v] < p.first) continue;
	    for (int i = 0; i < (int)G[v].size(); i++) {
		Edge &e = G[v][i];
		if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
		    dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
		    prevv[e.to] = v; preve[e.to] = i;
		    Q.push(pii(dist[e.to], e.to));
		}
	    }
	}
	if (dist[t] == INF) return -1;
	for (int v = 0; v < V; v++) {
	    h[v] += dist[v];
	}
	int d = f;
	for (int v = t; v != s; v = prevv[v]) {
	    d = min(d, G[prevv[v]][preve[v]].cap);
	}
	f -= d;
	res += d * h[t];
	for (int v = t; v != s; v = prevv[v]) {
	    Edge &e = G[prevv[v]][preve[v]];
	    e.cap -= d;
	    G[v][e.rev].cap += d;
	}
    }
    return res;
}

int main()
{
    int N;
    cin >> N;
    vector<int> p(N);
    for (int i = 0; i < N; i++) {
        cin >> p[i];
    }

    int S = 2*N, T = S + 1;
    V = T + 1;
    for (int i = 0; i < N; i++) {        
        add_edge(S, i, 1, 0);
        add_edge(i + N, T, 1, 0);
        for (int j = 0; j < N; j++) {
            if (p[i]-1 != j) {
                add_edge(i, j + N, 1, (p[i]) * abs(i - j));
            }
        }
    }
    cout << min_cost_flow(S, T, N) << endl;
    return 0;
}
### Prompt

Please create a solution in Cpp to the following problem:

G --Derangement / Derangement

Story

Person D is doing research on permutations. At one point, D found a permutation class called "Derangement". "It's cool to have a perfect permutation !!! And it starts with D !!!", the person of D who had a crush on Chunibyo decided to rewrite all the permutations given to him.

Problem

Given a permutation of length n, p = (p_1 p_2 ... p_n). The operation of swapping the i-th element and the j-th element requires the cost of (p_i + p_j) \ times | i-j |. At this time, find the minimum cost required to make p into a perfect permutation using only the above swap operation.

However, the fact that the permutation q is a perfect permutation means that q_i \ neq i holds for 1 \ leq i \ leq n. For example, (5 3 1 2 4) is a perfect permutation, but (3 2 5 4 1) is not a perfect permutation because the fourth number is 4.

Input

The input consists of the following format.


n
p_1 p_2 ... p_n

The first row consists of one integer representing the length n of the permutation. The second line consists of n integers, and the i-th integer represents the i-th element of the permutation p. Each is separated by a single blank character.

Constraints:

* 2 \ leq n \ leq 100
* 1 \ leq p_i \ leq n, i \ neq j ⇔ p_i \ neq p_j



Output

Print the minimum cost to sort p into a complete permutation on one line. Be sure to start a new line at the end of the line.

Sample Input 1


Five
1 2 3 5 4

Sample Output 1


7

After swapping 1 and 2, swapping 1 and 3 yields (2 3 1 5 4), which is a complete permutation.

Sample Input 2


Five
5 3 1 2 4

Sample Output 2


0

It is a perfect permutation from the beginning.

Sample Input 3


Ten
1 3 4 5 6 2 7 8 9 10

Sample Output 3


38





Example

Input

5
1 2 3 5 4


Output

7

### Response

```cpp
#include <bits/stdc++.h>

using namespace std;

#define MAX_V 514
#define INF 1e9
typedef pair<int, int> pii;

struct Edge {
    int to, cap, cost, rev;
    Edge(int to, int cap, int cost, int rev) :
        to(to), cap(cap), cost(cost), rev(rev) {}
};

int V, h[MAX_V], dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
vector<Edge> G[MAX_V];

void add_edge(int from, int to, int cap, int cost)
{
    G[from].push_back(Edge(to, cap, cost, G[to].size()));
    G[to].push_back(Edge(from, 0, -cost, G[from].size()-1));
}

int min_cost_flow(int s, int t, int f)
{
    int res = 0;
    fill(h, h+V, 0);
    while (f > 0) {
	priority_queue<pii, vector<pii>, greater<pii>> Q;
	fill(dist, dist+V, INF);
	dist[s] = 0;
	Q.push(pii(0, s));
	while (!Q.empty()) {
	    pii p = Q.top(); Q.pop();
	    int v = p.second;
	    if (dist[v] < p.first) continue;
	    for (int i = 0; i < (int)G[v].size(); i++) {
		Edge &e = G[v][i];
		if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
		    dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
		    prevv[e.to] = v; preve[e.to] = i;
		    Q.push(pii(dist[e.to], e.to));
		}
	    }
	}
	if (dist[t] == INF) return -1;
	for (int v = 0; v < V; v++) {
	    h[v] += dist[v];
	}
	int d = f;
	for (int v = t; v != s; v = prevv[v]) {
	    d = min(d, G[prevv[v]][preve[v]].cap);
	}
	f -= d;
	res += d * h[t];
	for (int v = t; v != s; v = prevv[v]) {
	    Edge &e = G[prevv[v]][preve[v]];
	    e.cap -= d;
	    G[v][e.rev].cap += d;
	}
    }
    return res;
}

int main()
{
    int N;
    cin >> N;
    vector<int> p(N);
    for (int i = 0; i < N; i++) {
        cin >> p[i];
    }

    int S = 2*N, T = S + 1;
    V = T + 1;
    for (int i = 0; i < N; i++) {        
        add_edge(S, i, 1, 0);
        add_edge(i + N, T, 1, 0);
        for (int j = 0; j < N; j++) {
            if (p[i]-1 != j) {
                add_edge(i, j + N, 1, (p[i]) * abs(i - j));
            }
        }
    }
    cout << min_cost_flow(S, T, N) << endl;
    return 0;
}
```