Problem: You are given a sequence a_1, a_2, …, a_n of non-negative integers.

You need to find the largest number m of triples (i_1, j_1, k_1), (i_2, j_2, k_2), ..., (i_m, j_m, k_m) such that:

  * 1 ≤ i_p < j_p < k_p ≤ n for each p in 1, 2, …, m;
  * a_{i_p} = a_{k_p} = 0, a_{j_p} ≠ 0;
  * all a_{j_1}, a_{j_2}, …, a_{j_m} are different;
  * all i_1, j_1, k_1, i_2, j_2, k_2, …, i_m, j_m, k_m are different.

Input

The first line of input contains one integer t (1 ≤ t ≤ 500 000): the number of test cases.

The first line of each test case contains one integer n (1 ≤ n ≤ 500 000).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n).

The total sum of n is at most 500 000.

Output

For each test case, print one integer m: the largest number of proper triples that you can find.

Example

Input


8
1
1
2
0 0
3
0 1 0
6
0 0 1 2 0 0
6
0 1 0 0 1 0
6
0 1 3 2 0 0
6
0 0 0 0 5 0
12
0 1 0 2 2 2 0 0 3 3 4 0


Output


0
0
1
2
1
1
1
2

Note

In the first two test cases, there are not enough elements even for a single triple, so the answer is 0.

In the third test case we can select one triple (1, 2, 3).

In the fourth test case we can select two triples (1, 3, 5) and (2, 4, 6).

In the fifth test case we can select one triple (1, 2, 3). We can't select two triples (1, 2, 3) and (4, 5, 6), because a_2 = a_5.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
pi readpi(ll off = 0) {
  ll first, second;
  cin >> first >> second;
  return pi(first + off, second + off);
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
vvc<ll> readGraph(ll n, ll m) {
  vvc<ll> g(n);
  for (ll i = ll(0); i < ll(m); i++) {
    ll first, second;
    cin >> first >> second;
    first--;
    second--;
    g[first].push_back(second);
    g[second].push_back(first);
  }
  return g;
}
vvc<ll> readTree(ll n) { return readGraph(n, n - 1); }
ll sub(ll n, ll m, vc<pi> input) {
  vector<vi> sejm(m + 1);
  vi cnt(m + 1, 0);
  for (ll i = ll(0); i < ll(n); i++) {
    ll l = input[i].first + 1, r = input[i].second;
    sejm[l].push_back(r);
    cnt[l]++;
  }
  for (ll i = m; i >= 1; i--) cnt[i - 1] += cnt[i];
  ll edgeL = -1, mn = cnt[0];
  for (ll i = ll(0); i < ll(m); i++) {
    mn = min(mn - 1, cnt[i + 1] - 1);
    if (mn < 0) break;
    edgeL = i;
  }
  priority_queue<ll> pq;
  for (ll i = m; i >= 0; i--) {
    if (i <= edgeL) pq.pop();
    for (auto t : sejm[i]) pq.push(t);
  }
  cnt.assign(m + 1, 0);
  while (!pq.empty()) {
    ll t = pq.top();
    pq.pop();
    cnt[t]++;
  }
  for (ll i = ll(0); i < ll(m); i++) cnt[i + 1] += cnt[i];
  ll edgeR = m;
  mn = cnt[m];
  for (ll i = m - 1; i >= 0; i--) {
    mn = min(mn - 1, cnt[i] - 1);
    if (mn < 0) break;
    edgeR = i;
  }
  return min(m, (edgeL + 1) + (m - edgeR));
}
void slv() {
  ll n;
  cin >> n;
  vi first = readvi(n);
  ll z = count(first.begin(), first.end(), 0);
  vi vs;
  for (auto v : first)
    if (v) vs.push_back(v);
  mkuni(vs);
  if (z <= 1) {
    print(0);
    return;
  }
  ll h = z / 2;
  ll x = -1, y = -1;
  vi lf(n, -1), rt(n, -1);
  {
    ll cnt = 0;
    for (ll i = ll(0); i < ll(n); i++) {
      if (first[i] == 0) {
        if (cnt == h - 1) x = i;
        cnt++;
        chmin(cnt, h);
      } else {
        lf[i] = cnt;
      }
    }
  }
  {
    ll cnt = 0;
    for (ll i = ll(n) - 1; i >= ll(0); i--) {
      if (first[i] == 0) {
        if (cnt == h - 1) y = i;
        cnt++;
        chmin(cnt, h);
      } else {
        rt[i] = cnt;
      }
    }
  }
  ll s = ll(vs.size());
  vc<pi> input(s, pi(-1, h));
  for (ll i = ll(y) - 1; i >= ll(0); i--)
    if (first[i]) {
      ll j = lwb(vs, first[i]);
      chmax(input[j].first, lf[i] - 1);
    }
  for (ll i = ll(x); i < ll(n); i++)
    if (first[i]) {
      ll j = lwb(vs, first[i]);
      chmin(input[j].second, h - rt[i]);
    }
  for (ll i = ll(0); i < ll(s); i++) chmax(input[i].second, input[i].first + 1);
  void(0);
  print(sub(s, h, input));
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll t;
  cin >> t;
  for (ll _ = ll(0); _ < ll(t); _++) slv();
}