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)

INF = (1 << 31) - 1
def init
  x = 1
  while x < $n
    x <<= 1
  end
  $n = x
  $arr = Array.new(2*x-1, INF)
end

def update(i, x)
  i += $n - 1
  $arr[i] = x
  while i > 0
    i = (i - 1) / 2
    $arr[i] = $arr[i*2+1,2].min
  end
end

def query(a,b,k,l,r)
  if r <= a || b <= l then return INF
  end
  if a <= l && r <= b then return $arr[k]
  else
    vl = query(a, b, k*2+1, l, (l+r) / 2)
    vr = query(a, b, k*2+2, (l+r) / 2, r)
    return [vl, vr].min
  end
end

$n, q = gets.split.map(&:to_i)
init
q.times do
  cmd, x, y = gets.split.map(&:to_i)
  if cmd == 0 then update(x, y)
  else puts query(x, y+1, 0, 0, $n)
  end
end