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: Runtime Error)

class Seg
  def initialize ( n, init, &func)
    @tree = Array.new( 2**n - 1, init )
    @init = init
    @n    = n
    @func = func || lambda{|x,y| x < y}
  end

  def update (i, x)
    i = 2**(@n-1) - 1 + i
    @tree[i] = x

    while (i=parent(i))>=0
      a,b = kids(i).map{|x| @tree[x]}
      @tree[i] = @func.call(a, b) ? a : b
    end

  end

  def find ( s, t, k=0, i=0, j=@n-1 )
    return @init if t<i || j<s
    return @tree[k] if s<=i && j<=t

    a, b = kids(k)
    a, b = find(s, t, a, i, (i+j)/2), find(s, t, b, (i+j)/2+1, j)
    @func.call(a, b) ? a : b
  end

  private
  def parent(i)
    (i-1)/2
  end

  def kids(i)
    [2*i+1, 2*i+2]
  end
end

n, q = gets.split.map(&:to_i)
i = 1
while 2**i < n
  i += 1
end

seg  = Seg.new(i, 2**31-1) { |x,y| x < y }
q.times do
  com, x, y = gets.split.map(&:to_i)

  case com
  when 0
    seg.update(x, y)
  when 1
    puts seg.find(x,y)
  end
end