description: In fact, the problems E1 and E2 do not have much in common. You should probably think of them as two separate problems.
  
  You are given an integer array a[1 … n] = [a_1, a_2, …, a_n].
  
  Let us consider an empty [deque](https://tinyurl.com/pfeucbux) (double-ended queue). A deque is a data structure that supports adding elements to both the beginning and the end. So, if there are elements [3, 4, 4] currently in the deque, adding an element 1 to the beginning will produce the sequence [\color{red}{1}, 3, 4, 4], and adding the same element to the end will produce [3, 4, 4, \color{red}{1}].
  
  The elements of the array are sequentially added to the initially empty deque, starting with a_1 and finishing with a_n. Before adding each element to the deque, you may choose whether to add it to the beginning or to the end.
  
  For example, if we consider an array a = [3, 7, 5, 5], one of the possible sequences of actions looks like this:    1. |  add 3 to the beginning of the deque: |  deque has a sequence [\color{red}{3}] in it;   
  ---|---|---  
    2. |  add 7 to the end of the deque: |  deque has a sequence [3, \color{red}{7}] in it;   
    3. |  add 5 to the end of the deque: |  deque has a sequence [3, 7, \color{red}{5}] in it;   
    4. |  add 5 to the beginning of the deque: |  deque has a sequence [\color{red}{5}, 3, 7, 5] in it;   
    
  Find the minimal possible number of inversions in the deque after the whole array is processed. 
  
  An inversion in sequence d is a pair of indices (i, j) such that i < j and d_i > d_j. For example, the array d = [5, 3, 7, 5] has exactly two inversions — (1, 2) and (3, 4), since d_1 = 5 > 3 = d_2 and d_3 = 7 > 5 = d_4.
  
  Input
  
  The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.
  
  The next 2t lines contain descriptions of the test cases. 
  
  The first line of each test case description contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — array size. The second line of the description contains n space-separated integers a_i (-10^9 ≤ a_i ≤ 10^9) — elements of the array.
  
  It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
  
  Output
  
  Print t lines, each line containing the answer to the corresponding test case. The answer to a test case should be a single integer — the minimal possible number of inversions in the deque after executing the described algorithm.
  
  Example
  
  Input
  
  
  6
  4
  3 7 5 5
  3
  3 2 1
  3
  3 1 2
  4
  -1 2 2 -1
  4
  4 5 1 3
  5
  1 3 1 3 2
  
  
  Output
  
  
  2
  0
  1
  0
  1
  2
  
  Note
  
  One of the ways to get the sequence [5, 3, 7, 5] in the deque, containing only two inversions, from the initial array [3, 7, 5, 5] (the first sample test case) is described in the problem statement. 
  
  Also, in this example, you could get the answer of two inversions by simply putting each element of the original array at the end of the deque. In this case, the original sequence [3, 7, 5, 5], also containing exactly two inversions, will be in the deque as-is.
solution: import java.io.*;
  import java.util.*;
  
  import static java.lang.Math.*;
  import static java.util.Arrays.*;
  
  public class cf1579e2 {
  
      public static void main(String[] args) throws IOException {
          int t = ri();
          next: while (t --> 0) {
              int n = ri(), a[] = ria(n), sorted[][] = new int[n][2], inv[] = new int[n], invinv[] = new int[n];
              for (int i = 0; i < n; ++i) {
                  sorted[i][0] = a[i];
                  sorted[i][1] = i;
              }
              sort(sorted, (x, y) -> x[0] - y[0]);
              sgt sgt = new sgt(n, Integer::sum, 0);
              Set<Integer> upds = new HashSet<>();
              for (int i = n - 1; i >= 0; --i) {
                  if (i != n - 1 && sorted[i][0] != sorted[i + 1][0]) {
                      for (int j : upds) {
                          sgt.upd(j, 1);
                      }
                      upds.clear();
                  }
                  inv[sorted[i][1]] = sgt.qry(0, sorted[i][1] - 1);
                  upds.add(sorted[i][1]);
              }
              sgt = new sgt(n, Integer::sum, 0);
              upds.clear();
              for (int i = 0; i < n; ++i) {
                  if (i != 0 && sorted[i][0] != sorted[i - 1][0]) {
                      for (int j : upds) {
                          sgt.upd(j, 1);
                      }
                      upds.clear();
                  }
                  invinv[sorted[i][1]] += sgt.qry(0, sorted[i][1] - 1);
                  upds.add(sorted[i][1]);
              }
              long ans = 0;
              for (int i = 0; i < n; ++i) {
                  ans += min(inv[i], invinv[i]);
              }
  //            prln(inv);
  //            prln(invinv);
              prln(ans);
          }
          close();
      }
  
      @FunctionalInterface
      interface IntOperator {
          int merge(int a, int b);
      }
  
      @FunctionalInterface
      interface IntAction {
          void apply(int x);
      }
  
      static class sgt {
          IntOperator upd_op, qry_op;
          int n, sgt[], lazy[], id;
  
          sgt(int sz, IntOperator operator, int identity) {
              n = sz;
              sgt = new int[4 * n + 5];
              lazy = new int[4 * n + 5];
              upd_op = qry_op = operator;
              id = identity;
              int a[] = new int[n];
              fill(a, id);
              build(1, a, 0, n - 1);
          }
  
          sgt(int sz, IntOperator update_operator, IntOperator query_operator, int identity) {
              n = sz;
              sgt = new int[4 * n + 5];
              lazy = new int[4 * n + 5];
              upd_op = update_operator;
              qry_op = query_operator;
              id = identity;
              int a[] = new int[n];
              fill(a, id);
              build(1, a, 0, n - 1);
          }
  
          sgt(int[] a, IntOperator operator, int identity) {
              n = a.length;
              sgt = new int[4 * n + 5];
              lazy = new int[4 * n + 5];
              upd_op = qry_op = operator;
              id = identity;
              build(1, a, 0, n - 1);
          }
  
          sgt(int[] a, IntOperator update_operator, IntOperator query_operator, int identity) {
              n = a.length;
              sgt = new int[4 * n + 5];
              lazy = new int[4 * n + 5];
              upd_op = update_operator;
              qry_op = query_operator;
              id = identity;
              build(1, a, 0, n - 1);
          }
  
          void set(int i, int x) {
              set(1, i, x, 0, n - 1);
          }
  
          void upd(int i, int j, int x) {
              upd(1, i, j, x, 0, n - 1);
          }
  
          void upd(int i, int x) {
              upd(1, i, x, 0, n - 1);
          }
  
          int qry(int l, int r) {
              return qry(1, l, r, 0, n - 1);
          }
  
          int qry(int i) {
              return qry(1, i, i, 0, n - 1);
          }
  
          void set(int node, int i, int x, int l, int r) {
              push(node, l, r);
              if (l == r) {
                  sgt[node] = x;
              } else {
                  int m = l + (r - l) / 2;
                  if (i <= m) {
                      set(node << 1, i, x, l, m);
                  } else {
                      set(node << 1 | 1, i, x, m + 1, r);
                  }
                  pull(node);
              }
          }
  
          void upd(int node, int i, int x, int l, int r) {
              push(node, l, r);
              if (l == r) {
                  sgt[node] = upd_op.merge(sgt[node], x);
              } else {
                  int m = l + (r - l) / 2;
                  if (i <= m) {
                      upd(node << 1, i, x, l, m);
                  } else {
                      upd(node << 1 | 1, i, x, m + 1, r);
                  }
                  pull(node);
              }
          }
  
          void upd(int node, int i, int j, int x, int l, int r) {
              push(node, l, r);
              if (r < i || j < l) {
                  return;
              } else if (i <= l && r <= j) {
                  lazy[node] = x;
                  push(node, l, r);
              } else {
                  int m = l + (r - l) / 2;
                  upd(node << 1, i, j, x, l, m);
                  upd(node << 1 | 1, i, j, x, m + 1, r);
                  pull(node);
              }
          }
  
          int qry(int node, int i, int j, int l, int r) {
              push(node, l, r);
              if (r < i || j < l) {
                  return id;
              } else if (i <= l && r <= j) {
                  return sgt[node];
              } else {
                  int m = l + (r - l) / 2;
                  return qry_op.merge(qry(node << 1, i, j, l, m), qry(node << 1 | 1, i, j, m + 1, r));
              }
          }
  
          void build(int node, int[] a, int l, int r) {
              if (l == r) {
                  sgt[node] = a[l];
              } else {
                  int m = l + (r - l) / 2;
                  build(node << 1, a, l, m);
                  build(node << 1 | 1, a, m + 1, r);
                  pull(node);
              }
          }
  
          void pull(int node) {
              sgt[node] = qry_op.merge(sgt[node << 1], sgt[node << 1 | 1]);
          }
  
          void push(int node, int l, int r) {
              // sgt[node] += lazy[node] * (r - l + 1);
              if (l != r) {
                  // lazy[node << 1] += lazy[node];
                  // lazy[node << 1 | 1] += lazy[node];
              }
              lazy[node] = 0;
          }
  
          void traverse(IntAction a) {
              traverse(a, 1, 0, n - 1);
          }
  
          void traverse(IntAction a, int node, int l, int r) {
              push(node, l, r);
              if (l == r) {
                  a.apply(sgt[node]);
              } else {
                  int m = l + (r - l) / 2;
                  traverse(a, node << 1, l, m);
                  traverse(a, node << 1 | 1, m + 1, r);
              }
          }
      }
  
      static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
      static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
      static StringTokenizer input;
      static Random __r = new Random();
  
      // references
      // IBIG = 1e9 + 7
      // IMAX ~= 2e9
      // LMAX ~= 9e18
  
      // constants
      static final int IBIG = 1000000007;
      static final int IMAX = 2147483647;
      static final long LMAX = 9223372036854775807L;
      // math util
      static int minof(int a, int b, int c) {return min(a, min(b, c));}
      static int minof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
      static long minof(long a, long b, long c) {return min(a, min(b, c));}
      static long minof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
      static int maxof(int a, int b, int c) {return max(a, max(b, c));}
      static int maxof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
      static long maxof(long a, long b, long c) {return max(a, max(b, c));}
      static long maxof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
      static int powi(int a, int b) {if (a == 0) return 0; int ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
      static long powl(long a, int b) {if (a == 0) return 0; long ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
      static int fli(double d) {return (int) d;}
      static int cei(double d) {return (int) ceil(d);}
      static long fll(double d) {return (long) d;}
      static long cel(double d) {return (long) ceil(d);}
      static int gcd(int a, int b) {return b == 0 ? a : gcd(b, a % b);}
      static long gcd(long a, long b) {return b == 0 ? a : gcd(b, a % b);}
      static int[] exgcd(int a, int b) {if (b == 0) return new int[] {1, 0}; int[] y = exgcd(b, a % b); return new int[] {y[1], y[0] - y[1] * (a / b)};}
      static long[] exgcd(long a, long b) {if (b == 0) return new long[] {1, 0}; long[] y = exgcd(b, a % b); return new long[] {y[1], y[0] - y[1] * (a / b)};}
      static int randInt(int min, int max) {return __r.nextInt(max - min + 1) + min;}
      static long mix(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
      // array util
      static void reverse(int[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(long[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(double[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(char[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void shuffle(int[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void shuffle(long[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void shuffle(double[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void rsort(int[] a) {shuffle(a); sort(a);}
      static void rsort(long[] a) {shuffle(a); sort(a);}
      static void rsort(double[] a) {shuffle(a); sort(a);}
      static int[] copy(int[] a) {int[] ans = new int[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      // input
      static void r() throws IOException {input = new StringTokenizer(rline());}
      static int ri() throws IOException {return Integer.parseInt(rline());}
      static long rl() throws IOException {return Long.parseLong(rline());}
      static double rd() throws IOException {return Double.parseDouble(rline());}
      static int[] ria(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni(); return a;}
      static void ria(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni();}
      static int[] riam1(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1; return a;}
      static void riam1(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1;}
      static long[] rla(int n) throws IOException {long[] a = new long[n]; r(); for (int i = 0; i < n; ++i) a[i] = nl(); return a;}
      static void rla(long[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nl();}
      static double[] rda(int n) throws IOException {double[] a = new double[n]; r(); for (int i = 0; i < n; ++i) a[i] = nd(); return a;}
      static void rda(double[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nd();}
      static char[] rcha() throws IOException {return rline().toCharArray();}
      static void rcha(char[] a) throws IOException {int n = a.length, i = 0; for (char c : rline().toCharArray()) a[i++] = c;}
      static String rline() throws IOException {return __i.readLine();}
      static String n() {return input.nextToken();}
      static int rni() throws IOException {r(); return ni();}
      static int ni() {return Integer.parseInt(n());}
      static long rnl() throws IOException {r(); return nl();}
      static long nl() {return Long.parseLong(n());}
      static double rnd() throws IOException {r(); return nd();}
      static double nd() {return Double.parseDouble(n());}
      // output
      static void pr(int i) {__o.print(i);}
      static void prln(int i) {__o.println(i);}
      static void pr(long l) {__o.print(l);}
      static void prln(long l) {__o.println(l);}
      static void pr(double d) {__o.print(d);}
      static void prln(double d) {__o.println(d);}
      static void pr(char c) {__o.print(c);}
      static void prln(char c) {__o.println(c);}
      static void pr(char[] s) {__o.print(new String(s));}
      static void prln(char[] s) {__o.println(new String(s));}
      static void pr(String s) {__o.print(s);}
      static void prln(String s) {__o.println(s);}
      static void pr(Object o) {__o.print(o);}
      static void prln(Object o) {__o.println(o);}
      static void prln() {__o.println();}
      static void pryes() {prln("yes");}
      static void pry() {prln("Yes");}
      static void prY() {prln("YES");}
      static void prno() {prln("no");}
      static void prn() {prln("No");}
      static void prN() {prln("NO");}
      static boolean pryesno(boolean b) {prln(b ? "yes" : "no"); return b;};
      static boolean pryn(boolean b) {prln(b ? "Yes" : "No"); return b;}
      static boolean prYN(boolean b) {prln(b ? "YES" : "NO"); return b;}
      static void prln(int... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static void prln(long... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static void prln(double... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i); if (n >= 0) prln(iter.next()); else prln();}
      static void h() {prln("hlfd"); flush();}
      static void flush() {__o.flush();}
      static void close() {__o.close();}
  }