CF1787D

码力有待加强！

//1787 D. Game on Axis
#include <bits/stdc++.h>
/*
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
*/
using namespace std;

const double eps = 1e-10;
const double pi = 3.1415926535897932384626433832795;
const double eln = 2.718281828459045235360287471352;

#define f(i, a, b) for (int i = a; i <= b; i++)
#define scan(x) scanf("%d", &x)
#define mp make_pair
#define pb push_back
#define lowbit(x) (x&(-x))

#define fi first
#define se second
#define SZ(x) int((x).size())
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define summ(a) (accumulate(all(a), 0ll))

typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;

using ll=long long;

ll tt,n,a[(int)2e5+9],son[(int)2e5+9];
bitset<(int)2e5+9> vis;

struct dsu{
    vi fa,sz;
    dsu(int n){
        fa.resize(n+1),sz.resize(n+1);
        for(int i=1;i<=n;++i)fa[i]=i,sz[i]=1;
    }
    int fnd(int x){
        return fa[x]==x?x:fa[x]=fnd(fa[x]);
    }
    bool merge(int x ,int y){
        int oa=fnd(x),ob=fnd(y);
        if(oa!=ob){
            fa[ob]=oa,sz[oa]+=sz[ob];
            return true;
        }
        return false;
    }
};

vi g[(int)2e5+9];

ll dfs(ll u,ll &ans){
    ll res=0;
    for(auto it:g[u]){
        res+=dfs(it,ans);
        if(!vis[it])son[u]+=son[it];
    }
    ans+=res*son[u];
    son[u]+=!vis[u];
    return res+(vis[u]);
}

void solve(){
    cin>>n;
    dsu d(n);
    vector<int> cycle;
    f(i,1,n)cin>>a[i];
    f(i,1,n)a[i]+=i;
    f(i,1,n)if(1<=a[i]&&a[i]<=n){g[a[i]].push_back(i);}
    f(i,1,n)son[i]=0ll;
    bool ok=true;
    vis.reset();
    ll ans=0,cnt=0,sz=0,p=1,lst=1;
    for(;1<=p&&p<=n;vis[p]=1,lst=p,p=a[p],sz+=1)if(vis[p]){ok=false;break;}

    if(ok)dfs(lst,ans);
    vis.reset();
    for(int i=1;i<=n;++i){
        if(1<=a[i]&&a[i]<=n)if(!d.merge(i,a[i]))cycle.push_back(d.fnd(i));
    }
    for(auto it:cycle)vis[d.fnd(it)]=1;
    for(int i=1,x;i<=n;++i)x=d.fnd(i),cnt+=(x!=d.fnd(1)&&!vis[x]);
    if(!ok)ans+=(cnt+1ll+n)*sz;
    else {
        ans+=(cnt+1ll+n)*sz+(n-sz)*(2ll*n+1ll)+(sz)*(sz-1ll)/2;

    }
    cout<<ans<<"\n";
    f(i,1,n)g[i].clear();
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>tt;
    f(sb,1,tt)solve();
    return 0;
}