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

inputFormat

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).

outputFormat

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

样例

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

2147483647
5

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