Problem:
RMQ and RUQ

Write a program which manipulates a sequence A = {a0, a1, . . . , an−1} with the following operations:

update(s, t, x): change as, as+1, ..., at to x.

find(s, t): report the minimum element in as, as+1, ..., at.

Note that the initial values of ai (i = 0, 1, . . . , n−1) are 231-1.

Input

n q
query1
query2
:
queryq

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query queryi is given in the following format:

0 s t x

or

1 s t

The first digit represents the type of the query. '0' denotes update(s, t, x) and '1' denotes find(s, t).

Output

For each find operation, print the minimum value.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

0 ≤ s ≤ t < n

0 ≤ x < 231−1

Sample Input 1

3 5
0 0 1 1
0 1 2 3
0 2 2 2
1 0 2
1 1 2

Sample Output 1

1
2

Sample Input 2

1 3
1 0 0
0 0 0 5
1 0 0

Sample Output 2

2147483647
5

Solution in Ruby (judge verdict: Accepted)

def rmq(a, b, k, l, r)
  return MAX if r <= a || b <= l
  return $d[k] if $d[k]
  m = (l+r)/2
  vl = rmq(a, b, 2*k+1, l, m)
  vr = rmq(a, b, 2*k+2, m, r)
  return vl < vr ? vl : vr
end

def update(s, t, x, k, l, r)
  if s == l && t == r then
    $d[k] = x
  else
    if $d[k] then
      $d[2*k+1] = $d[2*k+2] = $d[k]
      $d[k] = nil
    end
    m = (l + r)/2
    if t <= m then
      update(s, t, x, 2*k+1, l, m)
    elsif m <= s then
      update(s, t, x, 2*k+2, m, r)
    else
      update(s, m, x, 2*k+1, l, m)
      update(m, t, x, 2*k+2, m, r)
    end
  end
end

MAX = 2**31-1
n, q = gets.split.map(&:to_i)

m = 1
while m < n
  m *= 2
end

$d = Array.new(2*m-1){MAX}
q.times{
  com, s, t, x = gets.split.map(&:to_i)
  case com
  when 0
    update(s, t+1, x, 0, 0, m)
  when 1
    p rmq(s, t+1, 0, 0, m)
  end
}