#include <bits/stdc++.h>
#define PB push_back
#define sz(x) ((int)x.size())
#define ft first
#define sd second
#define all(x) x.begin(),x.end()
#define l2 array<ll,2>
using namespace std;
typedef long long ll;
const int N = 100100;
const int oo = int(2e9);
const ll OO = 1e18;
const int md = int(1e9) + 7;
vector<int> v[2];
int n;
ll x[N], ans = OO, pref_sum, suf_sum;
l2 fen[2][N];
void update(int tp, ll ps, int vl){
ll mem = ps * vl;
ps = lower_bound(all(v[tp]), ps) - v[tp].begin();
for (; ps < sz(v[tp]); ps = (ps | (ps + 1))) {
fen[tp][ps][0] += mem;
fen[tp][ps][1] += vl;
}
}
l2 get_fen(int tp, ll ps){
l2 res = {0, 0};
ps = upper_bound(all(v[tp]), ps) - v[tp].begin() - 1;
for (; ps >= 0; ps = (ps & (ps + 1)) - 1){
res[0] += fen[tp][ps][0];
res[1] += fen[tp][ps][1];
}
return res;
}
ll get(int id, ll ht){
ll cur = abs(x[id] - ht);
if (id > 0) {
l2 cr = get_fen(0, ht + (n - 1 - id));
ll ost = pref_sum - cr[0];
cur -= cr[0] - ((ll(n) - 1ll - ll(id)) * cr[1]);
cur += ht * cr[1];
cr[1] = id - cr[1];
cur += ost - ((ll(n) - 1ll - ll(id)) * cr[1]);
cur -= ht * cr[1];
}
if (id < n - 1){
l2 cr = get_fen(1, ht + id);
// cerr << cr[0] << " " << cr[1] << '\n';
ll ost = suf_sum - cr[0];
cur -= cr[0] - (ll(id) * cr[1]);
cur += ht * cr[1];
cr[1] = (n - 1 - id) - cr[1];
cur += ost - (ll(id) * cr[1]);
cur -= ht * cr[1];
}
return cur;
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0);
#ifdef _LOCAL
freopen("in.txt","r",stdin);
#endif // _LOCAL
cin >> n;
for (int i = 0; i < n; i++) {
cin >> x[i];
v[0].PB(x[i] + (n - 1 - i));
v[1].PB(x[i] + i);
}
sort(all(v[0]));
sort(all(v[1]));
v[0].resize(unique(all(v[0])) - v[0].begin());
v[1].resize(unique(all(v[1])) - v[1].begin());
for (int i = 0; i < n; i++) {
update(1, x[i] + i, 1);
suf_sum += x[i] + i;
}
for (int i = 0; i < n; i++){
update(1, x[i] + i, -1);
suf_sum -= x[i] + i;
ll l = max(i + 1, n - i), r = ll(1e9);
while (l + 5 < r){
ll md = (l + r) >> 1;
if (get(i, md) < get(i, md + 1))
r = md;
else l = md + 1;
}
for (ll j = l; j <= r; j++)
ans = min(ans, get(i, j));
update(0, x[i] + (n - 1 - i), 1);
pref_sum += x[i] + (n - 1 - i);
}
cout << ans;
return 0;
}
