import java.util.*;
import java.util.zip.*;
import java.util.List;
import java.util.regex.*;
import java.util.concurrent.*;
import java.util.concurrent.atomic.*;
import java.util.concurrent.locks.*;
import javax.swing.*;
import javax.swing.event.*;
import javax.swing.text.*;
import javax.swing.table.*;
import java.io.*;
import java.net.*;
import java.lang.reflect.*;
import java.lang.ref.*;
import java.lang.management.*;
import java.security.*;
import java.security.spec.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import javax.imageio.*;
import java.math.*;
// see: https://en.wikipedia.org/wiki/Order_statistic_tree
class main {

static class LogNArray<A> extends RandomAccessAbstractList<A> {

  private transient Entry<A> root;

  /**
   * The number of entries in the tree
   */
  //private transient int size = 0;

  /**
   * The number of structural modifications to the tree.
   */
  private transient int modCount = 0;

  // Query Operations

  public int size() {
    return root == null ? 0 : root.size;
  }

  public boolean contains(Object value) {
    for (Entry<A> e = getFirstEntry(); e != null; e = successor(e))
      if (eq(value, e.value))
        return true;
    return false;
  }

  public A get(int idx) {
    Entry<A> p = getEntry(idx);
    return p == null ? null : p.value;
  }

  int subTreeSize(Entry<A> e) { return e == null ? 0 : e.size; }

  final Entry<A> getEntry(int idx) {
    if (idx < 0 || idx >= size())
      throw new IndexOutOfBoundsException(idx + " / " + size());
    Entry<A> p = root;
    while (true) {
      int sizeLeft = subTreeSize(p.left);
      if (idx < sizeLeft)
        { p = p.left; continue; }
      idx -= sizeLeft;
      if (idx == 0) return p;
      idx--;
      p = p.right;
    }
  }

  /*public A put(Int key, A value) {
      Entry<A> t = root;
      if (t == null) {
          compare(key, key); // type (and possibly null) check

          root = new Entry<>(key, value, null);
          //size = 1;
          modCount++;
          return null;
      }
      int cmp;
      Entry<A> parent;
      // split comparator and comparable paths
      Comparator<? super Int> cpr = comparator;
      if (cpr != null) {
          do {
              parent = t;
              cmp = cpr.compare(key, t.key);
              if (cmp < 0)
                  t = t.left;
              else if (cmp > 0)
                  t = t.right;
              else
                  return t.setValue(value);
          } while (t != null);
      }
      else {
          if (key == null)
              throw new NullPointerException();
          @SuppressWarnings("unchecked")
              Comparable<? super Int> k = (Comparable<? super Int>) key;
          do {
              parent = t;
              cmp = k.compareTo(t.key);
              if (cmp < 0)
                  t = t.left;
              else if (cmp > 0)
                  t = t.right;
              else
                  return t.setValue(value);
          } while (t != null);
      }
      Entry<A> e = new Entry<>(key, value, parent);
      if (cmp < 0)
          parent.left = e;
      else
          parent.right = e;
      fixAfterInsertion(e);
      //size++;
      modCount++;
      return null;
  }*/

  /*public A remove(int idx) {
    Entry<A> p = getEntry(key);
    if (p == null)
        return null;

    A oldValue = p.value;
    deleteEntry(p);
    return oldValue;
  }*/

  public void clear() {
      modCount++;
      //size = 0;
      root = null;
  }

  // Red-black mechanics

  private static final boolean RED   = false;
  private static final boolean BLACK = true;

  /**
   * Node in the Tree.  Doubles as a means to pass key-value pairs back to
   * user (see Map.Entry).
   */

  static final class Entry<A> {
      int size = 1; // entry count of subtree
      //Int key;
      A value;
      Entry<A> left;
      Entry<A> right;
      Entry<A> parent;
      boolean color = BLACK;

      /**
       * Make a new cell with given value and parent, and with
       * {@code null} child links, size 1, and BLACK color.
       */
      Entry(A value, Entry<A> parent) {
          this.value = value;
          this.parent = parent;
      }
  }

  final Entry<A> getFirstEntry() {
      Entry<A> p = root;
      if (p != null)
          while (p.left != null)
              p = p.left;
      return p;
  }

  final Entry<A> getLastEntry() {
      Entry<A> p = root;
      if (p != null)
          while (p.right != null)
              p = p.right;
      return p;
  }

  static <Integer,A> LogNArray.Entry<A> successor(Entry<A> t) {
      if (t == null)
          return null;
      else if (t.right != null) {
          Entry<A> p = t.right;
          while (p.left != null)
              p = p.left;
          return p;
      } else {
          Entry<A> p = t.parent;
          Entry<A> ch = t;
          while (p != null && ch == p.right) {
              ch = p;
              p = p.parent;
          }
          return p;
      }
  }

  static <Integer,A> Entry<A> predecessor(Entry<A> t) {
      if (t == null)
          return null;
      else if (t.left != null) {
          Entry<A> p = t.left;
          while (p.right != null)
              p = p.right;
          return p;
      } else {
          Entry<A> p = t.parent;
          Entry<A> ch = t;
          while (p != null && ch == p.left) {
              ch = p;
              p = p.parent;
          }
          return p;
      }
  }

  /**
   * Balancing operations.
   *
   * Implementations of rebalancings during insertion and deletion are
   * slightly different than the CLR version.  Rather than using dummy
   * nilnodes, we use a set of accessors that deal properly with null.  They
   * are used to avoid messiness surrounding nullness checks in the main
   * algorithms.
   */

  private static <Integer,A> boolean colorOf(Entry<A> p) {
      return (p == null ? BLACK : p.color);
  }

  private static <Integer,A> Entry<A> parentOf(Entry<A> p) {
      return (p == null ? null: p.parent);
  }

  private static <Integer,A> void setColor(Entry<A> p, boolean c) {
      if (p != null)
          p.color = c;
  }

  private static <Integer,A> Entry<A> leftOf(Entry<A> p) {
      return (p == null) ? null: p.left;
  }

  private static <Integer,A> Entry<A> rightOf(Entry<A> p) {
      return (p == null) ? null: p.right;
  }

  /** From CLR */
  private void rotateLeft(Entry<A> p) {
      if (p != null) {
          Entry<A> r = p.right;
          p.right = r.left;
          if (r.left != null)
              r.left.parent = p;
          r.parent = p.parent;
          if (p.parent == null)
              root = r;
          else if (p.parent.left == p)
              p.parent.left = r;
          else
              p.parent.right = r;
          r.left = p;
          p.parent = r;
      }
  }

  /** From CLR */
  private void rotateRight(Entry<A> p) {
      if (p != null) {
          Entry<A> l = p.left;
          p.left = l.right;
          if (l.right != null) l.right.parent = p;
          l.parent = p.parent;
          if (p.parent == null)
              root = l;
          else if (p.parent.right == p)
              p.parent.right = l;
          else p.parent.left = l;
          l.right = p;
          p.parent = l;
      }
  }

  /** From CLR */
  private void fixAfterInsertion(Entry<A> x) {
      x.color = RED;

      while (x != null && x != root && x.parent.color == RED) {
          if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
              Entry<A> y = rightOf(parentOf(parentOf(x)));
              if (colorOf(y) == RED) {
                  setColor(parentOf(x), BLACK);
                  setColor(y, BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  x = parentOf(parentOf(x));
              } else {
                  if (x == rightOf(parentOf(x))) {
                      x = parentOf(x);
                      rotateLeft(x);
                  }
                  setColor(parentOf(x), BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  rotateRight(parentOf(parentOf(x)));
              }
          } else {
              Entry<A> y = leftOf(parentOf(parentOf(x)));
              if (colorOf(y) == RED) {
                  setColor(parentOf(x), BLACK);
                  setColor(y, BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  x = parentOf(parentOf(x));
              } else {
                  if (x == leftOf(parentOf(x))) {
                      x = parentOf(x);
                      rotateRight(x);
                  }
                  setColor(parentOf(x), BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  rotateLeft(parentOf(parentOf(x)));
              }
          }
      }
      root.color = BLACK;
  }

  /**
   * Delete node p, and then rebalance the tree.
   */
  private void deleteEntry(Entry<A> p) {
      modCount++;
      //size--;

      // If strictly internal, copy successor's element to p and then make p
      // point to successor.
      if (p.left != null && p.right != null) {
          Entry<A> s = successor(p);
          p.value = s.value;
          p = s;
      } // p has 2 children

      // Start fixup at replacement node, if it exists.
      Entry<A> replacement = (p.left != null ? p.left : p.right);

      if (replacement != null) {
          // Link replacement to parent
          replacement.parent = p.parent;
          if (p.parent == null)
              root = replacement;
          else if (p == p.parent.left)
              p.parent.left  = replacement;
          else
              p.parent.right = replacement;

          // Null out links so they are OK to use by fixAfterDeletion.
          p.left = p.right = p.parent = null;

          // Fix replacement
          if (p.color == BLACK)
              fixAfterDeletion(replacement);
      } else if (p.parent == null) { // return if we are the only node.
          root = null;
      } else { //  No children. Use self as phantom replacement and unlink.
          if (p.color == BLACK)
              fixAfterDeletion(p);

          if (p.parent != null) {
              if (p == p.parent.left)
                  p.parent.left = null;
              else if (p == p.parent.right)
                  p.parent.right = null;
              p.parent = null;
          }
      }
  }

  /** From CLR */
  private void fixAfterDeletion(Entry<A> x) {
      while (x != root && colorOf(x) == BLACK) {
          if (x == leftOf(parentOf(x))) {
              Entry<A> sib = rightOf(parentOf(x));

              if (colorOf(sib) == RED) {
                  setColor(sib, BLACK);
                  setColor(parentOf(x), RED);
                  rotateLeft(parentOf(x));
                  sib = rightOf(parentOf(x));
              }

              if (colorOf(leftOf(sib))  == BLACK &&
                  colorOf(rightOf(sib)) == BLACK) {
                  setColor(sib, RED);
                  x = parentOf(x);
              } else {
                  if (colorOf(rightOf(sib)) == BLACK) {
                      setColor(leftOf(sib), BLACK);
                      setColor(sib, RED);
                      rotateRight(sib);
                      sib = rightOf(parentOf(x));
                  }
                  setColor(sib, colorOf(parentOf(x)));
                  setColor(parentOf(x), BLACK);
                  setColor(rightOf(sib), BLACK);
                  rotateLeft(parentOf(x));
                  x = root;
              }
          } else { // symmetric
              Entry<A> sib = leftOf(parentOf(x));

              if (colorOf(sib) == RED) {
                  setColor(sib, BLACK);
                  setColor(parentOf(x), RED);
                  rotateRight(parentOf(x));
                  sib = leftOf(parentOf(x));
              }

              if (colorOf(rightOf(sib)) == BLACK &&
                  colorOf(leftOf(sib)) == BLACK) {
                  setColor(sib, RED);
                  x = parentOf(x);
              } else {
                  if (colorOf(leftOf(sib)) == BLACK) {
                      setColor(rightOf(sib), BLACK);
                      setColor(sib, RED);
                      rotateLeft(sib);
                      sib = leftOf(parentOf(x));
                  }
                  setColor(sib, colorOf(parentOf(x)));
                  setColor(parentOf(x), BLACK);
                  setColor(leftOf(sib), BLACK);
                  rotateRight(parentOf(x));
                  x = root;
              }
          }
      }

      setColor(x, BLACK);
  }

  /**
   * Finds the level down to which to assign all nodes BLACK.  This is the
   * last `full' level of the complete binary tree produced by buildTree.
   * The remaining nodes are colored RED. (This makes a `nice' set of
   * color assignments wrt future insertions.) This level number is
   * computed by finding the number of splits needed to reach the zeroeth
   * node.
   *
   * @param size the (non-negative) number of keys in the tree to be built
   */
  private static int computeRedLevel(int size) {
      return 31 - Integer.numberOfLeadingZeros(size + 1);
  }
}
static boolean eq(Object a, Object b) {
  return a == null ? b == null : a == b || b != null && a.equals(b);
}




static String str(Object o) {
  return o == null ? "null" : o.toString();
}

static String str(char[] c) {
  return new String(c);
}


abstract static class RandomAccessAbstractList<A> extends AbstractList<A> implements RandomAccess {
}
}