p02350 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.

Constraints

* 1 ≤ n ≤ 100000
* 1 ≤ q ≤ 100000
* 0 ≤ s ≤ t < n
* 0 ≤ x < 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.

Examples

Input

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


Output

1
2


Input

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


Output

2147483647
5
```python
import math
from collections import deque


class SegmentTree:
    __slots__ = ["rank", "elem_size", "tree_size", "tree", "lazy", "default_value"]

    def __init__(self, a: list, default: int):
        self.default_value = default
        real_size = len(a)
        self.rank = math.ceil(math.log2(real_size))
        self.elem_size = 1 << self.rank
        self.tree_size = 2 * self.elem_size
        self.tree = [default]*self.elem_size + a + [default]*(self.elem_size - real_size)
        self.lazy = [None]*self.tree_size
        # self.init_tree()

    def init_tree(self):
        tree = self.tree
        for i in range(self.elem_size-1, 0, -1):
            left, right = tree[i << 1], tree[(i << 1)+1]
            # ===== change me =====
            tree[i] = left if left < right else right

    def process_query(self, l: int, r: int, value: int = None):
        '''[x, y)'''
        tree, lazy, elem_size, rank = self.tree, self.lazy, self.elem_size, self.rank-1
        l, r, targets, p_l, p_r, l_rank, r_rank = l+elem_size, r+elem_size, deque(), 0, 0, 0, 0
        t_ap = targets.append

        while l < r:
            if l & 1:
                t_ap(l)
                p_l = p_l or l >> 1
                l_rank = l_rank or rank
                l += 1
            if r & 1:
                r -= 1
                t_ap(r)
                p_r = p_r or r >> 1
                r_rank = r_rank or rank
            l >>= 1
            r >>= 1
            rank -= 1

        deepest = (p_l, p_r)

        paths = [[p_l >> n for n in range(l_rank-1, -1, -1)], [p_r >> n for n in range(r_rank-1, -1, -1)]]

        for a in paths:
            for i in a:
                if lazy[i] is None:
                    continue
                # ===== change me =====
                tree[i] = lazy[i]
                if i < elem_size:
                    lazy[i << 1] = lazy[i]
                    lazy[(i << 1)+1] = lazy[i]
                lazy[i] = None

        result = self.default_value
        for i in targets:
            v = value if value is not None else lazy[i]
            # ===== change me =====
            if v is not None:
                if i < elem_size:
                    lazy[i << 1] = v
                    lazy[(i << 1)+1] = v
                tree[i] = v
                lazy[i] = None
            if result > tree[i]:
                result = tree[i]

        self.update_tree(deepest)

        return result

    def update_tree(self, indexes: tuple):
        ''' ????????????lazy?????¨????????¬????????§???????????¨???????????¨???????????? '''

        tree, lazy = self.tree, self.lazy

        for k in indexes:
            while k > 0:
                left, right = k << 1, (k << 1)+1
                # ===== change me =====
                l_value = tree[left] if lazy[left] is None else lazy[left]
                r_value = tree[right] if lazy[right] is None else lazy[right]
                tree[k] = l_value if l_value < r_value else r_value

                k >>= 1


n, q = map(int, input().split())
rmq = SegmentTree([2**31-1]*n, 2**31-1)
ans = []
append = ans.append
for _ in [0]*q:
    l = list(map(int, input().split()))
    if l[0] == 0:
        rmq.process_query(l[1], l[2]+1, l[3])
    else:
        a = rmq.process_query(l[1], l[2]+1)
        append(a)

print("\n".join([str(n) for n in ans]))
```