Problem:
Range Minimum Query (RMQ)

Write a program which manipulates a sequence A = {a0, a1, . . . , an-1} with the following operations:

find(s, t): report the minimum element in as, as+1, . . . ,at.

update(i, x): change ai to x.

Note that the initial values of ai (i = 0, 1, . . . , n−1) are 231-1.

Input

n q
com0 x0 y0
com1 x1 y1
...
comq−1 xq−1 yq−1

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes update(xi, yi) and '1' denotes find(xi, yi).

Output

For each find operation, print the minimum element.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

If comi is 0, then 0 ≤ xi < n, 0 ≤ yi < 231-1.

If comi is 1, then 0 ≤ xi < n, 0 ≤ yi < n.

Sample Input 1

3 5
0 0 1
0 1 2
0 2 3
1 0 2
1 1 2

Sample Output 1

1
2

Sample Input 2

1 3
1 0 0
0 0 5
1 0 0

Sample Output 2

2147483647
5

Solution in Python3 (judge verdict: Time Limit Exceeded)

import math
num,query = (int(n) for n in input().split(' '))
table = [2**31 - 1 for n in range(num)]
sqrttable = []
sqrtnum = math.floor(math.sqrt(num))
tempmin = float("inf")
for t in range(num):
    if t % sqrtnum == sqrtnum - 1:
        tempmin = min(table[t],tempmin)
        sqrttable.append(tempmin)
    elif t == num - 1:
        tempmin = min(table[t],tempmin)
        sqrttable.append(tempmin)
    else:
        tempmin = min(table[t],tempmin)

for q in range(query):
    #print(sqrtnum,table,sqrttable)
    temp = [int(n) for n in input().split(' ')]
    if temp[0] == 0:
        table[temp[1]] = temp[2]
        tempmin = float("inf")
        for tm in range(sqrtnum*(temp[1]//sqrtnum),min(num,sqrtnum*(temp[1]//sqrtnum + 1))):
            tempmin = min(table[tm],tempmin)
        sqrttable[temp[1]//sqrtnum] = tempmin
    else:
        tempmin = float("inf")
        if temp[1] % sqrtnum != 0:
            for ini in range(temp[1],min(temp[2]+1,sqrtnum * math.ceil(temp[1] / sqrtnum))):
                tempmin = min(tempmin,table[ini])
        newtemp2 = temp[2] + 1
        for sqt in range(math.ceil(temp[1] / sqrtnum),newtemp2 // sqrtnum):
            tempmin = min(sqrttable[sqt],tempmin)
        if temp[2] % sqrtnum != sqrtnum -1:
            for end in range(max(temp[1],sqrtnum * (temp[2]//sqrtnum)),temp[2]+1):
                tempmin = min(tempmin,table[end])
        #print(tempmin,sqrtnum,temp[1],temp[2],table,sqrttable)
        print(tempmin)