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 RMQ
  def initialize(n, inf = (1 << 30) - 1 + (1 << 30))
    @n = n, @l = 1, @inf = inf
    while @l < n
      @l <<= 1
    end
    @data = Array.new(@l * 2, @inf)
  end

  def update(i, x)
    i += @l
    @data[i] = x
    i >>= 1
    while i > 0
      @data[i] = min(@data[i * 2], @data[i * 2 + 1])
      i >>= 1
    end
    true
  end

  # minimum of [l, r)
  def query(l, r)
    _query(l, r, 1, 0, @l)
  end

  def [](k)
    @data[@l + k]
  end

  private

  def _query(l, r, k, sl, sr)
    return @inf if sr <= l || r <= sl
    return @data[k] if l <= sl && sr <= r
    dl = _query(l, r, k * 2, sl, (sl + sr) / 2)
    dr = _query(l, r, k * 2 + 1, (sl + sr) / 2, sr)
    min(dl, dr)
  end

  def min(a, b)
    return (a > b ? b : a)
  end
end


n, q = gets.split.map(&:to_i)
rmq = RMQ.new(n)
ans = []
q.times do
  com, x, y = gets.split.map(&:to_i)
  if com == 0
    rmq.update(x, y)
  else
    ans << rmq.query(x, y + 1)
  end
end
puts ans