description: Alice has recently received an array a_1, a_2, ..., a_n for her birthday! She is very proud of her array, and when she showed her friend Bob the array, he was very happy with her present too!
  
  However, soon Bob became curious, and as any sane friend would do, asked Alice to perform q operations of two types on her array:
  
    * 1 x y: update the element a_x to y (set a_x = y). 
    * 2 l r: calculate how many non-decreasing subarrays exist within the subarray [a_l, a_{l+1}, ..., a_r]. More formally, count the number of pairs of integers (p,q) such that l ≤ p ≤ q ≤ r and a_p ≤ a_{p+1} ≤ ... ≤ a_{q-1} ≤ a_q. 
  
  
  
  Help Alice answer Bob's queries!
  
  Input
  
  The first line contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^5) — the size of the array, and the number of queries, respectively.
  
  The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the elements of Alice's array.
  
  The next q lines consist of three integers each. The first integer of the i-th line is t_i, the operation being performed on the i-th step (t_i = 1 or t_i = 2).
  
  If t_i = 1, the next two integers are x_i and y_i (1 ≤ x_i ≤ n; 1 ≤ y_i ≤ 10^9), updating the element at position x_i to y_i (setting a_{x_i} = y_i).
  
  If t_i = 2, the next two integers are l_i and r_i (1 ≤ l_i ≤ r_i ≤ n), the two indices Bob asks Alice about for the i-th query.
  
  It's guaranteed that there is at least one operation of the second type.
  
  Output
  
  For each query of type 2, print a single integer, the answer to the query.
  
  Example
  
  Input
  
  
  5 6
  3 1 4 1 5
  2 2 5
  2 1 3
  1 4 4
  2 2 5
  1 2 6
  2 2 5
  
  
  Output
  
  
  6
  4
  10
  7
  
  Note
  
  For the first query, l = 2 and r = 5, and the non-decreasing subarrays [p,q] are [2,2], [3,3], [4,4], [5,5], [2,3] and [4,5].
solution: import java.io.*;
  import java.util.*;
  
  public class Div21567E {
  
  	static long[][] t;
  	static long[] a;
  	
  	public static void main(String[] args) throws IOException {
  
  		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  		PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
  		StringTokenizer st = new StringTokenizer(br.readLine());
  		
  		int n = Integer.parseInt(st.nextToken());
  		int q = Integer.parseInt(st.nextToken());
  		a = new long[n];
  		
  		st = new StringTokenizer(br.readLine());
  		
  		for(int i = 0; i < n; i++)
  			a[i] = Integer.parseInt(st.nextToken());
  		
  		t = new long[4 * n][7];
  		
  		build(1, 0, n-1);
  		
  		for(int i = 0; i < q; i++) {
  			
  			st = new StringTokenizer(br.readLine());
  			int type = Integer.parseInt(st.nextToken());
  			int xl = Integer.parseInt(st.nextToken());
  			int yr = Integer.parseInt(st.nextToken());
  			
  			if(type == 1) {
  				
  				update(1, 0, n-1, xl-1, yr);
  				
  			}else {
  				
  				long[] res = sum(1, 0, n-1, xl-1, yr-1);
  				
  				if(res[6] == 1) {
  					
  					pw.println(res[4]);
  					
  				}else {
  					
  					pw.println((res[4] + (res[3] * (res[3] + 1) / 2)));
  					
  				}
  				
  				//pw.flush();
  				
  			}
  			
  		}
  
  		pw.flush();
  		pw.close();
  		
  	}
  	
  	//0 = leftmost val
  	//1 = leftmost len
  	//2 = rightmost val
  	//3 = rightmost len
  	//4 = left sub count (excluding right)
  	//5 = right sub count (excluding left)
  	//6 = 0 == broken, 1 == whole
  	static void build(int v, int tl, int tr) {
  	    if (tl == tr) {
  	        t[v][0] = t[v][2] = a[tl];
  	        t[v][1] = t[v][3] = t[v][4] = t[v][5] = t[v][6] = 1;
  	        //System.out.println("Leaf: " + tl + " " + a[tl] + " | " + t[v][0] + " " + t[v][1] + " " + t[v][2] + " " + t[v][3] + " " + t[v][4] + " " + t[v][5] + " " + t[v][6]);
  	    } else {
  	        int tm = (tl + tr) / 2;
  	        build(v*2, tl, tm);
  	        build(v*2+1, tm+1, tr);
  	        
  	        //setting left and right most vals
  	        t[v][0] = t[v*2][0];
  	        t[v][2] = t[v*2+1][2];	        
  	        //check to see if they decrease into each other
  	        if(t[v*2][2] <= t[v*2+1][0]) {
  	        	
  	        	//System.out.println("Merging: " + t[v*2][2] + " " + t[v*2+1][0]);
  	        	
  	        	//create mid segment ERROR add parentheses around numb
  	        	long midseg = (t[v*2][3] + t[v*2+1][1]) * (t[v*2][3] + t[v*2+1][1] + 1) / 2;
  	        	
  	        	//set temporary whole flag
  	        	t[v][6] = 1;
  	        	
  	        	//check if left segment is whole
  	        	if(t[v*2][6] == 1) {
  	        		
  	        		//if whole then add on additional length from right
  	        		t[v][1] = t[v*2][3] + t[v*2+1][1];
  	        		
  	        		if(t[v*2+1][6] == 1) {
  	        			
  	        			t[v][4] = midseg;	        			
  	        			
  	        		}else {
  	        			
  	        			t[v][4] = midseg + t[v*2+1][4] - (t[v*2+1][1] * (t[v*2+1][1] + 1) / 2);
  	        			
  	        		}
  	        		
  	        	}else {
  	        		
  	        		//otherwise set left length to outside length of left
  	        		t[v][1] = t[v*2][1];
  	        		//whole of segment cannot be true is part is not whole
  	        		t[v][6] = 0;
  	        		
  	        		if(t[v*2+1][6] == 1) {
  	        			
  	        			t[v][4] = t[v*2][4];	        			
  	        			
  	        		}else {
  	        			
  	        			t[v][4] = t[v*2][4] + midseg + t[v*2+1][4] - (t[v*2+1][1] * (t[v*2+1][1] + 1) / 2);
  	        			
  	        		}
  	        			        		
  	        	}
  	        	
  	        	//check if right segment is whole
  	        	if(t[v*2+1][6] == 1) {
  	        		
  	        		//if whole then add on additional length from left
  	        		t[v][3] = t[v*2][3] + t[v*2+1][1];
  	        		
  	        		if(t[v*2][6] == 1) {
  	        			
  	        			t[v][5] = midseg;	        			
  	        			
  	        		}else {
  	        				        				  
  	        			//error here for triang numb we are adding instead of mult
  	        			t[v][5] = midseg + t[v*2][5] - (t[v*2][3] * (t[v*2][3] + 1) / 2);
  	        			
  	        			//System.out.println("Action: " + midseg + " " + t[v*2][3]);
  	        			
  	        		}
  	        		
  	        	}else {
  	        		
  	        		//otherwise set right length to outside length of right
  	        		t[v][3] = t[v*2+1][3];
  	        		//whole of segment cannot be true is part is not whole
  	        		t[v][6] = 0;
  	        		
  	        		if(t[v*2][6] == 1) {
  	        			
  	        			t[v][5] = t[v*2+1][5];	        			
  	        			
  	        		}else {
  	        			
  	        			t[v][5] = t[v*2+1][5] + midseg + t[v*2][5] - (t[v*2][3] * (t[v*2][3] + 1) / 2);
  	        			
  	        		}
  	        			        		
  	        	}        	
  	        	
  	        }else {
  	        	
  	        	//set outside lengths
  		        t[v][1] = t[v*2][1];
  		        t[v][3] = t[v*2+1][3];
  		        
  		        //set broken
  		        t[v][6] = 0;
  		        
  		        //set sums
  		        
  		        //System.out.println("Setting: " + t[v*2][4] + " " + t[v*2][6] + " " + t[v*2][3]);
  		        
  		        t[v][4] = t[v*2][4] + ((t[v*2][6] == 0) ? (t[v*2][3] * (t[v*2][3] + 1) / 2) : 0) + ((t[v*2+1][6] == 0) ? t[v*2+1][4] : 0);
  		        t[v][5] = t[v*2+1][5] + ((t[v*2+1][6] == 0) ? (t[v*2+1][1] * (t[v*2+1][1] + 1) / 2) : 0) + ((t[v*2][6] == 0) ? t[v*2][5] : 0);
  	        	
  	        }
  	        
  	        //System.out.println("Branch: " + tl + " " + tr + " | " + t[v][0] + " " + t[v][1] + " " + t[v][2] + " " + t[v][3] + " " + t[v][4] + " " + t[v][5] + " " + t[v][6]);
  	        
  	    }
  	}
  	
  	static void update(int v, int tl, int tr, int pos, int new_val) {
  	    if (tl == tr) {
  	    	t[v][0] = t[v][2] = new_val;
  	        t[v][1] = t[v][3] = 1;
  	    } else {
  	        int tm = (tl + tr) / 2;
  	        if (pos <= tm)
  	            update(v*2, tl, tm, pos, new_val);
  	        else
  	            update(v*2+1, tm+1, tr, pos, new_val);
  	      //setting left and right most vals
  	        t[v][0] = t[v*2][0];
  	        t[v][2] = t[v*2+1][2];	        
  	        //check to see if they decrease into each other
  	        if(t[v*2][2] <= t[v*2+1][0]) {
  	        	
  	        	//create mid segment
  	        	long midseg = (t[v*2][3] + t[v*2+1][1]) * (t[v*2][3] + t[v*2+1][1] + 1) / 2;
  	        	
  	        	//set temporary whole flag
  	        	t[v][6] = 1;
  	        	
  	        	//check if left segment is whole
  	        	if(t[v*2][6] == 1) {
  	        		
  	        		//if whole then add on additional length from right
  	        		t[v][1] = t[v*2][3] + t[v*2+1][1];
  	        		
  	        		if(t[v*2+1][6] == 1) {
  	        			
  	        			t[v][4] = midseg;	        			
  	        			
  	        		}else {
  	        			
  	        			t[v][4] = midseg + t[v*2+1][4] - (t[v*2+1][1] * (t[v*2+1][1] + 1) / 2);
  	        			
  	        		}
  	        		
  	        	}else {
  	        		
  	        		//otherwise set left length to outside length of left
  	        		t[v][1] = t[v*2][1];
  	        		//whole of segment cannot be true is part is not whole
  	        		t[v][6] = 0;
  	        		
  	        		if(t[v*2+1][6] == 1) {
  	        			
  	        			t[v][4] = t[v*2][4];	        			
  	        			
  	        		}else {
  	        			
  	        			t[v][4] = t[v*2][4] + midseg + t[v*2+1][4] - (t[v*2+1][1] * (t[v*2+1][1] + 1) / 2);
  	        			
  	        		}
  	        			        		
  	        	}
  	        	
  	        	//check if right segment is whole
  	        	if(t[v*2+1][6] == 1) {
  	        		
  	        		//if whole then add on additional length from left
  	        		t[v][3] = t[v*2][3] + t[v*2+1][1];
  	        		
  	        		if(t[v*2][6] == 1) {
  	        			
  	        			t[v][5] = midseg;	        			
  	        			
  	        		}else {
  	        			
  	        			t[v][5] = midseg + t[v*2][5] - (t[v*2][3] * (t[v*2][3] + 1) / 2);
  	        			
  	        		}
  	        		
  	        	}else {
  	        		
  	        		//otherwise set right length to outside length of right
  	        		t[v][3] = t[v*2+1][3];
  	        		//whole of segment cannot be true is part is not whole
  	        		t[v][6] = 0;
  	        		
  	        		if(t[v*2][6] == 1) {
  	        			
  	        			t[v][5] = t[v*2+1][5];	        			
  	        			
  	        		}else {
  	        			
  	        			t[v][5] = t[v*2+1][5] + midseg + t[v*2][5] - (t[v*2][3] * (t[v*2][3] + 1) / 2);
  	        			
  	        		}
  	        			        		
  	        	}
  	        	
  	        	
  	        	
  	        }else {
  	        	
  	        	//set outside lengths
  		        t[v][1] = t[v*2][1];
  		        t[v][3] = t[v*2+1][3];
  		        
  		        //set broken
  		        t[v][6] = 0;
  		        
  		        //set sums
  		        t[v][4] = t[v*2][4] + ((t[v*2][6] == 0) ? (t[v*2][3] * (t[v*2][3] + 1) / 2) : 0) + ((t[v*2+1][6] == 0) ? t[v*2+1][4] : 0);
  		        t[v][5] = t[v*2+1][5] + ((t[v*2+1][6] == 0) ? (t[v*2+1][1] * (t[v*2+1][1] + 1) / 2) : 0) + ((t[v*2][6] == 0) ? t[v*2][5] : 0);
  	        	
  	        }
  	    }
  	}
  
  	static long[] sum(int v, int tl, int tr, int l, int r) {
  	    if (l > r) 
  	        return null;
  	    if (l == tl && r == tr) {
  	        return t[v];
  	    }
  	    int tm = (tl + tr) / 2;
  	    
  	    long[] sega = sum(v*2, tl, tm, l, Math.min(r, tm));
  	    long[] segb = sum(v*2+1, tm+1, tr, Math.max(l, tm+1), r);
  	    long[] segc = new long[7];
  	    
  	    if(sega == null)
  	    	return segb;
  	    
  	    if(segb == null)
  	    	return sega;
  	    
  	    //setting left and right most vals
  	    segc[0] = sega[0];
  	    segc[2] = segb[2];	        
          //check to see if they decrease into each other
          if(sega[2] <= segb[0]) {
          	
          	//create mid segment
          	long midseg = (sega[3] + segb[1]) * (sega[3] + segb[1] + 1) / 2;
          	
          	//set temporary whole flag
          	segc[6] = 1;
          	
          	//check if left segment is whole
          	if(sega[6] == 1) {
          		
          		//if whole then add on additional length from right
          		segc[1] = sega[3] + segb[1];
          		
          		if(segb[6] == 1) {
          			
          			segc[4] = midseg;	        			
          			
          		}else {
          			
          			segc[4] = midseg + segb[4] - (segb[1] * (segb[1] + 1) / 2);
          			
          		}
          		
          	}else {
          		
          		//otherwise set left length to outside length of left
          		segc[1] = sega[1];
          		//whole of segment cannot be true is part is not whole
          		segc[6] = 0;
          		
          		if(segb[6] == 1) {
          			
          			segc[4] = sega[4];	        			
          			
          		}else {
          			
          			segc[4] = sega[4] + midseg + segb[4] - (segb[1] * (segb[1] + 1) / 2);
          			
          		}
          			        		
          	}
          	
          	//check if right segment is whole
          	if(segb[6] == 1) {
          		
          		//if whole then add on additional length from left
          		segc[3] = sega[3] + segb[1];
          		
          		if(sega[6] == 1) {
          			
          			segc[5] = midseg;	        			
          			
          		}else {
          			
          			segc[5] = midseg + sega[5] - (sega[3] * (sega[3] + 1) / 2);
          			
          		}
          		
          	}else {
          		
          		//otherwise set right length to outside length of right
          		segc[3] = segb[3];
          		//whole of segment cannot be true is part is not whole
          		segc[6] = 0;
          		
          		if(sega[6] == 1) {
          			
          			segc[5] = segb[5];	        			
          			
          		}else {
          			
          			segc[5] = segb[5] + midseg + sega[5] - (sega[3] * (sega[3] + 1) / 2);
          			
          		}
          			        		
          	}
          	
          	
          	
          }else {
          	
          	//set outside lengths
          	segc[1] = sega[1];
          	segc[3] = segb[3];
  	        
  	        //set broken
          	segc[6] = 0;
  	        
  	        //set sums
          	segc[4] = sega[4] + ((sega[6] == 0) ? (sega[3] * (sega[3] + 1) / 2) : 0) + ((segb[6] == 0) ? segb[4] : 0);
  	        segc[5] = segb[5] + ((segb[6] == 0) ? (segb[1] * (segb[1] + 1) / 2) : 0) + ((sega[6] == 0) ? sega[5] : 0);
          	
          }
          
          return segc;
  	    
  	}
  	
  }
  