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;
using ld = long double;
using db = double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <class T>
using V = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
const int MOD = 1e9 + 7;
const int MX = 5e5 + 5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1, 0, -1, 0}, yd[4] = {0, 1, 0, -1};
mt19937 rng(0);
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); }
template <class T>
bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T, class U>
T fstTrue(T lo, T hi, U first) {
  hi++;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo) / 2;
    first(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U first) {
  lo--;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo + 1) / 2;
    first(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
template <class T>
void remDup(vector<T>& v) {
  sort(begin(v), end(v));
  v.erase(unique(begin(v), end(v)), end(v));
}
template <class T, class U>
void erase(T& t, const U& u) {
  auto it = t.find(u);
  assert(it != end(t));
  t.erase(u);
}
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(AR<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(db& d) {
  str t;
  re(t);
  d = stod(t);
}
void re(ld& d) {
  str 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(AR<T, SZ>& x) {
  for (auto& a : x) re(a);
}
str to_string(char c) { return str(1, c); }
str to_string(const char* second) { return (str)second; }
str to_string(str second) { return second; }
str to_string(bool b) { return to_string((int)b); }
template <class T>
str to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
str to_string(vector<bool> v) {
  str res = "{";
  for (int i = (0); i < ((int)(v).size()); ++i) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ>
str to_string(bitset<SZ> b) {
  str res = "";
  for (int i = (0); i < (SZ); ++i) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
str to_string(pair<T, U> p);
template <class T>
str to_string(T v) {
  bool fst = 1;
  str res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
str to_string(pair<T, U> p) {
  return to_string(p.first) + " " + to_string(p.second);
}
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...);
}
void setIn(str second) { freopen(second.c_str(), "r", stdin); }
void setOut(str second) { freopen(second.c_str(), "w", stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str second = "") {
  unsyncIO();
  if ((int)(second).size()) {
    setIn(second + ".in"), setOut(second + ".out");
  }
}
int seg[1 << 20], lazy[1 << 20];
int calc(int ind) { return seg[ind] + lazy[ind]; }
void ad(int mn, int ind, int L, int R) {
  if (mn > R) return;
  if (mn <= L) {
    lazy[ind]++;
    return;
  }
  int M = (L + R) / 2;
  ad(mn, 2 * ind, L, M);
  ad(mn, 2 * ind + 1, M + 1, R);
  seg[ind] = min(calc(2 * ind), calc(2 * ind + 1));
}
vpi pairs;
void build(int ind, int L, int R) {
  lazy[ind] = 0;
  if (L == R) {
    seg[ind] = (int)(pairs).size() - L;
    return;
  }
  int M = (L + R) / 2;
  build(2 * ind, L, M);
  build(2 * ind + 1, M + 1, R);
  seg[ind] = min(calc(2 * ind), calc(2 * ind + 1));
  assert(seg[ind] == (int)(pairs).size() - R);
}
int qmin(int lo, int ind, int L, int R) {
  if (lo <= L) return calc(ind);
  if (R < lo) return MOD;
  int M = (L + R) / 2;
  return min(qmin(lo, 2 * ind, L, M), qmin(lo, 2 * ind + 1, M + 1, R)) +
         lazy[ind];
}
int n;
vi a;
vi zero;
vi todo[MX];
bool ok(int num) {
  pairs.clear();
  for (int i = (0); i < (num); ++i)
    pairs.push_back({zero[i], zero[(int)(zero).size() - num + i]});
  int lo = 0, hi = -1;
  vi LO(n + 1, (int)(pairs).size() + 1), HI(n + 1, 0);
  for (int i = (0); i < (n); ++i)
    if (a[i]) {
      while (lo < (int)(pairs).size() && pairs[lo].second < i) lo++;
      while (hi + 1 < (int)(pairs).size() && pairs[hi + 1].first <= i) hi++;
      if (lo <= hi) {
        if (lo == 0) {
          ckmax(HI[a[i]], hi + 1);
        } else {
          assert(hi == (int)(pairs).size() - 1);
          ckmin(LO[a[i]], lo + 1);
        }
      }
    }
  for (int i = (0); i < ((int)(pairs).size()); ++i) todo[i].clear();
  int abv = 0;
  for (int i = (1); i < (n + 1); ++i) {
    if (HI[i] == 0 && LO[i] == (int)(pairs).size() + 1) continue;
    todo[HI[i]].push_back(LO[i]);
    abv++;
  }
  build(1, 0, (int)(pairs).size());
  for (int i = (0); i < ((int)(pairs).size()); ++i) {
    for (auto& t : todo[i]) {
      abv--;
      ad(t, 1, 0, (int)(pairs).size());
    }
    if (i + abv + qmin(i, 1, 0, (int)(pairs).size()) < (int)(pairs).size()) {
      return 0;
    }
  }
  return 1;
}
void solve() {
  n = rng() % 10 + 1;
  a.clear();
  for (int j = (0); j < (n); ++j) {
    if (rng() & 1)
      a.push_back(0);
    else
      a.push_back(rng() % min(n, 3) + 1);
  }
  re(n);
  a.resize(n);
  re(a);
  zero.clear();
  for (int i = (0); i < (n); ++i)
    if (a[i] == 0) zero.push_back(i);
  int ans1 = lstTrue(1, (int)(zero).size() / 2, [&](int x) { return ok(x); });
  ps(ans1);
}
int main() {
  setIO();
  int t;
  re(t);
  for (int i = (0); i < (t); ++i) solve();
}