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)

class LazySegmentTreeBase
  def initialize(arr, l = 0, r = arr.size - 1)
    @l, @r = l, r
    @lazy = nil
    if l == r
      @agg = arr[l]
    else
      c = (l + r) / 2
      @left_child = self.class.new(arr, l, c)
      @right_child = self.class.new(arr, c + 1, r)
      @agg = aggregation_of(@left_child.agg, @right_child.agg)
    end
  end

  attr_reader :agg, :l, :r

  def update(l, r, x)
    if l == @l && r == @r
      defer(x)
    else
      force
      if r <= @left_child.r
        @left_child.update(l, r, x)
      elsif @right_child.l <= l
        @right_child.update(l, r, x)
      else
        @left_child.update(l, @left_child.r, x)
        @right_child.update(@right_child.l, r, x)
      end
      @left_child.force
      @right_child.force
      @agg = aggregation_of(@left_child.agg, @right_child.agg)
    end
  end

  def force
    return if !@lazy
    x = @lazy
    @lazy = nil
    whole_update(x)
    @left_child.update(@left_child.l, @left_child.r, x) if @left_child
    @right_child.update(@right_child.l, @right_child.r, x) if @right_child
  end

  def query(l, r)
    force
    return @agg if l == @l && r == @r
    if r <= @left_child.r
      return @left_child.query(l, r)
    elsif @right_child.l <= l
      return @right_child.query(l, r)
    else
      agg_left = @left_child.query(l, @left_child.r)
      agg_right = @right_child.query(@right_child.l, r)
      return aggregation_of(agg_left, agg_right)
    end
  end
end

class LazySegmentTree < LazySegmentTreeBase
  def initialize(arr, l = 0, r = arr.size - 1)
    super(arr, l, r)
  end

  def defer(x)
    @lazy = x
  end

  def whole_update(x)
    @agg = x
  end

  def aggregation_of(x, y)
    [x, y].min
  end
end

n, q = gets.split.map(&:to_i)
seg = LazySegmentTree.new(Array.new(n, 2 ** 31 - 1))
q.times do
  c, x, y, z = gets.split.map(&:to_i)
  if c == 0
    seg.update(x, y, z)
  else
    puts seg.query(x, y) 
  end
end