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 Ruby (judge verdict: Accepted)

class Bucket
  INF = 2 ** 31 - 1

  def initialize(n)
    @arr = Array.new(n){ INF }
    bucket_size = Math.sqrt(n).ceil
    @bucket = Array.new(bucket_size) { INF }
  end

  def update(i, val)
    @arr[i] = val
    bucket_idx = to_bucket_idx(i)

    if val < @bucket[bucket_idx]
      @bucket[bucket_idx] = val
    else
      @bucket[bucket_idx] = find_min(@arr, bucket_idx * @bucket.size, (bucket_idx + 1) * @bucket.size - 1)
    end
  end

  def query(i, j)
    i_bucket_idx = to_bucket_idx(i)
    j_bucket_idx = to_bucket_idx(j)

    return find_min(@arr, i, j) if (j_bucket_idx - i_bucket_idx) <= 2

    val = []
    val << find_min(@arr, i, (i_bucket_idx + 1) * @bucket.size - 1)
    val << find_min(@arr, (j_bucket_idx - 1) * @bucket.size, j)
    val << find_min(@bucket, i_bucket_idx + 1, j_bucket_idx - 1)

    val.min
  end

  private

  def find_min(arr, start_idx, end_idx)
    min = arr[start_idx]
    (start_idx..end_idx).each{|i| min = arr[i] if !arr[i].nil? && arr[i] < min }
    min
  end

  def to_bucket_idx(i)
    i / @bucket.size
  end
end

n, q = gets.split.map(&:to_i)
b = Bucket.new(n)

q.times do
  com, x, y = gets.split.map(&:to_i)

  case com
  when 0
    b.update(x, y)
  when 1
    puts b.query(x, y)
  end
end