Maximum Nested Array Depth

You are given a possibly nested array (list) in JSON format. Your task is to determine its maximum nesting depth.

The depth of a non-nested element is defined as 1. For an array that contains nested arrays, the depth is computed using the formula:

$$\text{depth} = 1 + \max(\text{depths of nested arrays})$$

For example, the array [1, [2, 3]] has a depth of 2, and [1, [2, [3, 4]]] has a depth of 3.

Note that even if some inner arrays are empty (e.g. []), they still count as an array and increase the depth accordingly.

inputFormat

The input consists of a single line containing a JSON array representation. The array may contain integers or other arrays nested arbitrarily.

Examples of valid inputs:

• [1, 2, 3]
• [1, [2, 3]]
• [1, [2, [3, 4]]]

outputFormat

Output the maximum depth (an integer) of the provided nested array on a single line.

## sample

[1,2,3]

1