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 C# (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
public partial class LibraryOfDataStructures{
	public static void Main(){
		string[] line = System.Console.ReadLine().Split(' ');
		int n = int.Parse(line[0]);
		int p = int.Parse(line[1]);

		decimal[] dt = new decimal[n];

		decimal f = (decimal)(Math.Pow(2, 31) - 1);
		List<int> list = new List<int>();
		for (int i = 0; i < n; i++)
		{
			dt[i] = f;
		}

		for (int k = 0; k < p; k++)
		{
			string[] line2 = System.Console.ReadLine().Split(' ');
			int cmd = int.Parse(line2[0]);
			int a = int.Parse(line2[1]);
			int b = int.Parse(line2[2]);

			switch (cmd)
			{
				case 0:
					// update
					dt[a] = b;
					list.Add(a);
					break;
				case 1:
					// find
					decimal min = f;
					if (b - a < list.Count)
					{
						for (int l = a; l <= b; l++)
						{
							if (min > dt[l])
							{
								min = dt[l];
							}
							if (min == 0)
							{
								break;
							}
						}
					}
					else
					{
						foreach (int l in list)
						{
							if (a <= l && l <= b)
							{
								if (min > dt[l])
								{
									min = dt[l];
								}
								if (min == 0)
								{
									break;
								}
							}
						}
					}
					System.Console.WriteLine(min.ToString("0"));
					break;
			}
		}
	}
}