Given two integer arrays arr1 and arr2, return the minimum number of operations (possibly zero) needed to make arr1 strictly increasing.

In one operation, you can choose two indices 0 <= i < arr1.length and 0 <= j < arr2.length and do the assignment arr1[i] = arr2[j].

If there is no way to make arr1 strictly increasing, return -1.

 

Example 1:


Input: arr1 = [1,5,3,6,7], arr2 = [1,3,2,4]

Output: 1

Explanation: Replace 5 with 2, then arr1 = [1, 2, 3, 6, 7].

Example 2:


Input: arr1 = [1,5,3,6,7], arr2 = [4,3,1]

Output: 2

Explanation: Replace 5 with 3 and then replace 3 with 4. arr1 = [1, 3, 4, 6, 7].

Example 3:


Input: arr1 = [1,5,3,6,7], arr2 = [1,6,3,3]

Output: -1

Explanation: You can't make arr1 strictly increasing.

 

Constraints: