The only difference between easy and hard versions is constraints.

There are n kids, each of them is reading a unique book. At the end of any day, the i-th kid will give his book to the p_i-th kid (in case of i = p_i the kid will give his book to himself). It is guaranteed that all values of p_i are distinct integers from 1 to n (i.e. p is a permutation). The sequence p doesn't change from day to day, it is fixed.

For example, if n=6 and p=[4, 6, 1, 3, 5, 2] then at the end of the first day the book of the 1-st kid will belong to the 4-th kid, the 2-nd kid will belong to the 6-th kid and so on. At the end of the second day the book of the 1-st kid will belong to the 3-th kid, the 2-nd kid will belong to the 2-th kid and so on.

Your task is to determine the number of the day the book of the i-th child is returned back to him for the first time for every i from 1 to n.

Consider the following example: p = [5, 1, 2, 4, 3]. The book of the 1-st kid will be passed to the following kids:

  * after the 1-st day it will belong to the 5-th kid, 
  * after the 2-nd day it will belong to the 3-rd kid, 
  * after the 3-rd day it will belong to the 2-nd kid, 
  * after the 4-th day it will belong to the 1-st kid. 



So after the fourth day, the book of the first kid will return to its owner. The book of the fourth kid will return to him for the first time after exactly one day.

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 1000) — the number of queries. Then q queries follow.

The first line of the query contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of kids in the query. The second line of the query contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n, all p_i are distinct, i.e. p is a permutation), where p_i is the kid which will get the book of the i-th kid.

It is guaranteed that ∑ n ≤ 2 ⋅ 10^5 (sum of n over all queries does not exceed 2 ⋅ 10^5).

Output

For each query, print the answer on it: n integers a_1, a_2, ..., a_n, where a_i is the number of the day the book of the i-th child is returned back to him for the first time in this query.

Example

Input


6
5
1 2 3 4 5
3
2 3 1
6
4 6 2 1 5 3
1
1
4
3 4 1 2
5
5 1 2 4 3


Output


1 1 1 1 1 
3 3 3 
2 3 3 2 1 3 
1 
2 2 2 2 
4 4 4 1 4 
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
#pragma GCC optimize("unroll-loops")
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<double, double>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<double>;
using vs = vector<string>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
const int di[4] = {-1, 0, 1, 0}, dj[4] = {0, 1, 0, -1};
const int di8[8] = {-1, -1, 0, 1, 1, 1, 0, -1},
          dj8[8] = {0, 1, 1, 1, 0, -1, -1, -1};
const ld PI = acos((ld)-1);
const ll INF = 1e18;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll randint(ll a, ll b) { return uniform_int_distribution<ll>(a, b)(rng); }
bool pow2(int i) { return i && (i & -i) == i; }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); }
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }
ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }
ll half(ll x) { return fdiv(x, 2); }
template <class T>
bool chmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool chmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
void remDup(vector<T>& v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), end(v));
}
template <class T, class U>
void remAll(vector<T>& v, U a) {
  v.erase(remove((v).begin(), (v).end(), a), v.end());
}
template <class T, class U>
T fstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = half(lo + hi);
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = half(lo + hi + 1);
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
template <class T, class U, class C>
string to_string(tuple<T, U, C> p);
template <class T, class U, class C, class D>
string to_string(tuple<T, U, C, D> p);
string to_string(char c) { return string(1, c); }
string to_string(bool b) { return to_string((int)b); }
string to_string(const char* s) { return (string)s; }
string to_string(string s) { return s; }
template <class T>
string to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
string to_string(vb v) {
  string res = "{";
  for (int i = (0); i < (((int)(v).size())); ++i) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ>
string to_string(bitset<SZ> b) {
  string res = "";
  for (int i = (0); i < (((int)(b).size())); ++i) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p);
template <class T>
string to_string(T v) {
  bool fst = 1;
  string res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p) {
  return to_string(p.first) + " " + to_string(p.second);
}
template <class T, class U, class C>
string to_string(tuple<T, U, C> p) {
  return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " +
         to_string(get<2>(p));
}
template <class T, class U, class C, class D>
string to_string(tuple<T, U, C, D> p) {
  return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " +
         to_string(get<2>(p)) + " " + to_string(get<3>(p));
}
template <class T, class U, class C>
void re(tuple<T, U, C>& p);
template <class T, class U, class C, class D>
void re(tuple<T, U, C, D>& p);
template <class T>
void re(complex<T>& c);
template <class T, class U>
void re(pair<T, U>& p);
template <class T>
void re(vector<T>& v);
template <class T, size_t SZ>
void re(array<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(double& d) {
  string t;
  re(t);
  d = stod(t);
}
void re(ld& d) {
  string t;
  re(t);
  d = stold(t);
}
template <class T, class... U>
void re(T& t, U&... u) {
  re(t);
  re(u...);
}
template <class T>
void re(complex<T>& c) {
  T a, b;
  re(a, b);
  c = {a, b};
}
template <class T, class U>
void re(pair<T, U>& p) {
  re(p.first, p.second);
}
template <class T>
void re(vector<T>& x) {
  for (auto& a : x) re(a);
}
template <class T, size_t SZ>
void re(array<T, SZ>& x) {
  for (auto& a : x) re(a);
}
template <class T, class U, class C>
void re(tuple<T, U, C>& p) {
  re(get<0>(p), get<1>(p), get<2>(p));
}
template <class T, class U, class C, class D>
void re(tuple<T, U, C, D>& p) {
  re(get<0>(p), get<1>(p), get<2>(p), get<3>(p));
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
struct chash {
  const uint64_t C = ll(2e18 * PI) + 71;
  const int RANDOM = rng();
  ll operator()(ll x) const { return __builtin_bswap64((x ^ RANDOM) * C); }
};
template <class T>
using V = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
template <class T>
using mpq = priority_queue<T, vector<T>, greater<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T, class U>
using um = unordered_map<T, U, chash>;
template <class T>
using us = unordered_set<T, chash>;
template <class T>
using PR = pair<T, T>;
const int MOD = 1e9 + 7;
template <int MOD, int RT>
struct mint {
  static const int mod = MOD;
  static constexpr mint rt() { return RT; }
  int v;
  explicit operator int() const { return v; }
  mint() { v = 0; }
  mint(ll _v) {
    v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
    if (v < 0) v += MOD;
  }
  friend bool operator==(const mint& a, const mint& b) { return a.v == b.v; }
  friend bool operator!=(const mint& a, const mint& b) { return !(a == b); }
  friend bool operator<(const mint& a, const mint& b) { return a.v < b.v; }
  friend void re(mint& a) {
    ll x;
    re(x);
    a = mint(x);
  }
  friend string to_string(mint a) { return to_string(a.v); }
  mint& operator+=(const mint& m) {
    if ((v += m.v) >= MOD) v -= MOD;
    return *this;
  }
  mint& operator-=(const mint& m) {
    if ((v -= m.v) < 0) v += MOD;
    return *this;
  }
  mint& operator*=(const mint& m) {
    v = (ll)v * m.v % MOD;
    return *this;
  }
  mint& operator/=(const mint& m) { return (*this) *= inv(m); }
  friend mint pow(mint a, ll p) {
    mint ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1) ans *= a;
    return ans;
  }
  friend mint inv(const mint& a) {
    assert(a.v != 0);
    return pow(a, MOD - 2);
  }
  mint operator-() const { return mint(-v); }
  mint& operator++() { return *this += 1; }
  mint& operator--() { return *this -= 1; }
  friend mint operator+(mint a, const mint& b) { return a += b; }
  friend mint operator-(mint a, const mint& b) { return a -= b; }
  friend mint operator*(mint a, const mint& b) { return a *= b; }
  friend mint operator/(mint a, const mint& b) { return a /= b; }
};
typedef mint<MOD, 5> mi;
vector<vector<mi>> scmb;
void genComb(int SZ) {
  scmb.assign(SZ, vector<mi>(SZ));
  scmb[0][0] = 1;
  for (int i = (1); i < (SZ); ++i)
    for (int j = (0); j < (i + 1); ++j)
      scmb[i][j] = scmb[i - 1][j] + (j ? scmb[i - 1][j - 1] : 0);
}
vi invs, fac, ifac;
void genFac(int SZ) {
  invs.resize(SZ), fac.resize(SZ), ifac.resize(SZ);
  invs[1] = fac[0] = ifac[0] = 1;
  for (int i = (2); i < (SZ); ++i)
    invs[i] = MOD - (ll)MOD / i * invs[MOD % i] % MOD;
  for (int i = (1); i < (SZ); ++i) {
    fac[i] = (ll)fac[i - 1] * i % MOD;
    ifac[i] = (ll)ifac[i - 1] * invs[i] % MOD;
  }
}
mi comb(int a, int b) {
  if (a < b || b < 0) return 0;
  return (ll)fac[a] * ifac[b] % MOD * ifac[a - b] % MOD;
}
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
using ul = unsigned long long;
ul modMul(ul a, ul b, const ul mod) {
  ll ret = a * b - mod * (ul)((ld)a * b / mod);
  return ret + ((ret < 0) - (ret >= (ll)mod)) * mod;
}
ul modPow(ul a, ul b, const ul mod) {
  if (b == 0) return 1;
  ul res = modPow(a, b / 2, mod);
  res = modMul(res, res, mod);
  return b & 1 ? modMul(res, a, mod) : res;
}
bool prime(ul n) {
  if (n < 2 || n % 6 % 4 != 1) return n - 2 < 2;
  ul A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
     s = __builtin_ctzll(n - 1), d = n >> s;
  for (auto& a : A) {
    ul p = modPow(a, d, n), i = s;
    while (p != 1 && p != n - 1 && a % n && i--) p = modMul(p, p, n);
    if (p != n - 1 && i != s) return 0;
  }
  return 1;
}
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void IOS(int n = 10, string s = "") {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout.precision(n);
  cerr.precision(n);
  cerr << fixed;
  cout << fixed;
  if (((int)(s).size())) {
    setIn(s + ".in"), setOut(s + ".out");
  }
}
const int mxN = 2e5 + 5;
struct DSU {
  vi e;
  void init(int N) { e = vi(N, -1); }
  int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
  bool sameSet(int a, int b) { return get(a) == get(b); }
  int size(int x) { return -e[get(x)]; }
  bool unite(int x, int y) {
    x = get(x), y = get(y);
    if (x == y) return 0;
    if (e[x] > e[y]) swap(x, y);
    e[x] += e[y];
    e[y] = x;
    return 1;
  }
};
void solve(int tt) {
  int n;
  re(n);
  vi a(n);
  re(a);
  DSU d;
  d.init(n);
  vi v;
  for (int i = (0); i < (n); ++i) {
    --a[i];
    d.unite(i, a[i]);
  }
  for (int i = (0); i < (n); ++i) v.push_back(d.size(i));
  ps(v);
}
int main() {
  IOS();
  int t = 1;
  re(t);
  for (int i = (0); i < (t); ++i) {
    solve(i + 1);
  }
}
