human
Can you solve the below in PYTHON?
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].

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Write me a Python program to print a single integer, the answer to the query?
assistant
#Here is Python program to print a single integer, the answer to the query.

import sys
import os
from io import BytesIO

if sys.version_info[0] < 3:
    sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))

f = sys.stdin
if os.environ.get('USER') == "loic":
    f = open("data.in")

line = lambda: f.readline().strip('\right\n').split()

def write(w):
    sys.stdout.write(w)
    sys.stdout.write("\n")

class Data:
    def __init__(self, pref, suff, first, last, sz, res):
        self.pref = pref
        self.suff = suff
        self.first = first
        self.last = last
        self.sz = sz
        self.res = res
        
    def __str__(self):
        d = self.__dict__
        res = ""
        for k,v in d.items():
            res += str(k) + " : " + str(v) + "\n"
        return res
        
def merge(a, b):
    #################################
    if a is None and b is not None:
        return b
    if b is None and a is not None:
        return a
    if a is None and b is None:
        return None
    #################################
    
    sz = a.sz + b.sz
    first = a.first
    last = b.last
    res = a.res + b.res
    
    pref = a.pref
    suff = b.suff
    
    if a.last <= b.first:
        res += a.suff * b.pref
        if a.suff == a.sz:
            pref = a.suff + b.pref
        if b.pref == b.sz:
            suff = b.pref + a.suff
    
    return Data(pref,suff,first,last,sz,res)
    
class SegmentTree:
    def __init__(self, arr):
        self.n = len(arr)
        self.sz = 1<<(self.n-1).bit_length()
        self.data = [None] * 2 * self.sz
        
        for i in range(self.n):
            self.data[self.sz + i] = arr[i]
        for i in range(self.sz - 1, 0, -1):
            self.data[i] = merge(self.data[i<<1], self.data[i<<1|1])
 
 
    def update(self, pos, new_val):
        i = self.sz + pos
        self.data[i] = new_val
     
        while i > 1:
            i >>= 1
            self.data[i] = merge(self.data[i<<1], self.data[i<<1|1])
        
    def query(self, l, r):
        tl = self.sz + l
        tr = self.sz + r + 1
        res_left = None
       ...