How to merge and aggregate values in 2 JSON files using jq?

I am using jq in a shell script to manipulate JSON files.

I have 2 files and I'd like to merge them into one file while also aggregating (sum) the values when names in the name/value pairs are the same.

As an example:

Input1.json

[  {"A": "Name 1","B": "1.1","C": "2"  },  {"A": "Name 2","B": "3.2","C": "4"  }]

Input2.json

[  {"A": "Name 2","B": "5","C": "6"  },  {"A": "Name 3","B": "7","C": "8"  }]

Expected result:

Output.json

[  {"A": "Name 1","B": "1.1","C": "2"  },  {"A": "Name 2","B": "8.2","C": "10"  },  {"A": "Name 3","B": "7","C": "8"  }]

I can use other tools other than jq but prefer to ultimately keep the solution contained into a shell script I can call from the Terminal.

Any help is appreciated. Thank you.