Problem: 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

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline
INF = 2**31 - 1

class LazySegmentTree:
    def __init__(self, n):
        LV = (n-1).bit_length()
        self.N0 = 2 ** LV
        self.data = [INF] * (2*self.N0)
        self.lazy = [None] * (2*self.N0)
        
    def gindex(self, l, r):
        L = l + self.N0; R = r + self.N0
        lm = (L // (L & -L)) >> 1
        rm = (R // (R & -R)) >> 1
    
        while L < R:
            if R <= rm:
                yield R
            if L <= lm:
                yield L
            
            L >>= 1; R >>= 1
        
        while L:
            yield L
            L >>= 1

    def propagates(self, *ids):
        for i in reversed(ids):
            v = self.lazy[i-1]
            
            if v is None:
                continue
            
            self.lazy[2*i-1] = self.data[2*i-1] = self.lazy[2*i] = self.data[2*i] = v
            self.lazy[i-1] = None

    def update(self, l, r, x):
        *ids, = self.gindex(l, r)
        self.propagates(*ids)

        L = self.N0 + l; R = self.N0 + r
        
        while L < R:
            if R & 1:
                R -= 1
                self.lazy[R-1] = self.data[R-1] = x
            if L & 1:
                self.lazy[L-1] = self.data[L-1] = x
                L += 1
                
            L >>= 1; R >>= 1
            
        for i in ids:
            self.data[i-1] = min(self.data[2*i-1], self.data[2*i])

    def query(self, l, r):
        self.propagates(*self.gindex(l, r))
        L = self.N0 + l; R = self.N0 + r

        s = INF
        
        while L < R:
            if R & 1:
                R -= 1
                s = min(s, self.data[R-1])
            if L & 1:
                s = min(s, self.data[L-1])
                L += 1
                
            L >>= 1; R >>= 1
            
        return s

n, q = map(int, input().split())
lst = LazySegmentTree(n)

for _ in range(q):
    que = list(map(int, input().split()))
    
    if que[0] == 0:
        s, t, x = que[1], que[2], que[3]
        lst.update(s, t+1, x)
    elif que[0] == 1:
        s, t = que[1], que[2]
        print(lst.query(s, t+1))