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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.*;
class main {
// This code has been contributed by 29AjayKumar
// from: https://www.geeksforgeeks.org/timsort/
static final int timSortIntArray_RUN = 32;
// this function sorts array from left index to
// to right index which is of size atmost RUN
static void timSortIntArray_insertionSort(int[] arr, int left, int right) {
for (int i = left + 1; i <= right; i++)
{
int temp = arr[i];
int j = i - 1;
while (j >= left && arr[j] > temp)
{
arr[j + 1] = arr[j];
j--;
}
arr[j + 1] = temp;
}
}
// merge function merges the sorted runs
static void timSortIntArray_merge(int[] arr, int l,
int m, int r) {
// original array is broken in two parts
// left and right array
int len1 = m - l + 1, len2 = r - m;
int[] left = new int[len1];
int[] right = new int[len2];
for (int x = 0; x < len1; x++)
{
left[x] = arr[l + x];
}
for (int x = 0; x < len2; x++)
{
right[x] = arr[m + 1 + x];
}
int i = 0;
int j = 0;
int k = l;
// after comparing, we merge those two array
// in larger sub array
while (i < len1 && j < len2)
{
if (left[i] <= right[j])
{
arr[k] = left[i];
i++;
}
else
{
arr[k] = right[j];
j++;
}
k++;
}
// copy remaining elements of left, if any
while (i < len1)
{
arr[k] = left[i];
k++;
i++;
}
// copy remaining element of right, if any
while (j < len2)
{
arr[k] = right[j];
k++;
j++;
}
}
// iterative Timsort function to sort the
// array[0...n-1] (similar to merge sort)
static void timSortIntArray(int[] arr) { timSortIntArray(arr, lIntArray(arr)); }
static void timSortIntArray(int[] arr, int n) {
// Sort individual subarrays of size RUN
for (int i = 0; i < n; i += timSortIntArray_RUN)
{
timSortIntArray_insertionSort(arr, i, Math.min((i + 31), (n - 1)));
}
// start merging from size RUN (or 32). It will merge
// to form size 64, then 128, 256 and so on ....
for (int size = timSortIntArray_RUN; size < n; size = 2 * size)
{
// pick starting point of left sub array. We
// are going to merge arr[left..left+size-1]
// and arr[left+size, left+2*size-1]
// After every merge, we increase left by 2*size
for (int left = 0; left < n; left += 2 * size)
{
// find ending point of left sub array
// mid+1 is starting point of right sub array
int mid = min(left + size - 1, n - 1);
int right = Math.min(left + 2 * size - 1, n - 1);
//if (right < mid || mid < left) fail("Overflow at " + n2(left) + "/" + size + ". mid=" + n2(mid) + ", right=" + n2(right));
// merge sub array arr[left.....mid] &
// arr[mid+1....right]
timSortIntArray_merge(arr, left, mid, right);
}
}
}
static int lIntArray(int[] a) {
return a == null ? 0 : a.length;
}
static int min(int a, int b) {
return Math.min(a, b);
}
static long min(long a, long b) {
return Math.min(a, b);
}
static float min(float a, float b) { return Math.min(a, b); }
static float min(float a, float b, float c) { return min(min(a, b), c); }
static double min(double a, double b) {
return Math.min(a, b);
}
static double min(double[] c) {
double x = Double.MAX_VALUE;
for (double d : c) x = Math.min(x, d);
return x;
}
static float min(float[] c) {
float x = Float.MAX_VALUE;
for (float d : c) x = Math.min(x, d);
return x;
}
static byte min(byte[] c) {
byte x = 127;
for (byte d : c) if (d < x) x = d;
return x;
}
static short min(short[] c) {
short x = 0x7FFF;
for (short d : c) if (d < x) x = d;
return x;
}
static int min(int[] c) {
int x = Integer.MAX_VALUE;
for (int d : c) if (d < x) x = d;
return x;
}
}