Find the largest number n positions away from n A sequel to this question.

Task

Given an array of positive integers, find the largest element k for which:


  There exists some positive integer distance n, so that the element in the array located n places to the left or right from k equals n.


The array is guaranteed to contain at least one element satisfying this condition.

The shortest code (in bytes) wins. You may choose whichever I/O format you like.

Example

Given the input

[4, 6, 7, 9, 3, 6, 5, 7, 2]


The eligible values are:


The 4, as there is a 7 located 7 positions to its right
The first 6, as there is a 3 located 3 positions to its right
The 3, as there is a 4 located 4 positions to its left
The 5, as there is a 2 located 2 positions to its right
The second 7, as there is a 3 located 3 positions to its left.


Of these values, the largest is 7.

Test cases

[1, 13] → 13
[2, 9, 8, 3, 72, 2] → 8
[5, 28, 14, 5, 6, 3, 4, 7] → 14
[1, 3, 5, 15, 4, 1, 2, 6, 7, 7] → 7
[5, 1, 3, 5, 2, 5, 5, 8, 5, 1, 5, 1, 2, 3] → 5
[5, 12, 2, 5, 4, 7, 3, 3, 6, 2, 10, 5, 5, 5, 4, 1, 8, 5] → 10
05AB1E, 21 bytes

vyN+Ny-})¹gL&lt;Ãv¹yè})Z


Explanation

v      }               # for each num in input
 yN+                   # push index + num
    Ny-                # push index - num
        )              # wrap stack in a list
         ¹gL&lt;Ã         # remove indices outside the range of input
              v¹yè})   # get list of elements in input at the remaining indices
                    Z  # get max


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