I have a databricks dataframe with the following schema:

DataFrame[id: string, created_at: timestamp, feedback_id: string, user_id: string, evaluation_id: string, evaluation_session_id: string, feedback_created_at: timestamp, evaluation_created_at: timestamp, evaluation_session_created_at: timestamp, __processed_at__: timestamp, arena_id: string, model_a_id: string, model_b_id: string, winner: string, evaluation_order: int, messages: array<struct<index:int,user:struct<evaluation_session_id:string,id:string,evaluation_id:string,role:string,parent_message_ids:array<string>,content:array<struct<type:string,text:string,image:string,mimeType:string>>,model_id:string,status:string,created_at:timestamp,updated_at:timestamp,message_order:int,modalities:array<string>,token_count:int,markdown_element_counts:map<string,int>,__processed_at__:timestamp,index:int>,model_a:struct<evaluation_session_id:string,id:string,evaluation_id:string,role:string,parent_message_ids:array<string>,content:array<struct<type:string,text:string,image:string,mimeType:string>>,model_id:string,status:string,created_at:timestamp,updated_at:timestamp,message_order:int,modalities:array<string>,token_count:int,markdown_element_counts:map<string,int>,__processed_at__:timestamp,index:int>,model_b:struct<evaluation_session_id:string,id:string,evaluation_id:string,role:string,parent_message_ids:array<string>,content:array<struct<type:string,text:string,image:string,mimeType:string>>,model_id:string,status:string,created_at:timestamp,updated_at:timestamp,message_order:int,modalities:array<string>,token_count:int,markdown_element_counts:map<string,int>,__processed_at__:timestamp,index:int>>>, input_modalities: array<string>, output_modalities: array<string>, context_input_modalities: array<string>, context_output_modalities: array<string>, evaluation_session_title: string, evaluation_session_mode: string, arena_slug: string, arena_capability_requirements: variant, arena_info: struct<id:string,name:string,slug:string,capability_requirements:variant,updated_at:timestamp>, model_a_public_name: string, model_b_public_name: string, model_a_info: struct<id:string,public_name:string,organization:string,provider:string,visibility:string,status:string,capabilities:variant,updated_at:timestamp>, model_b_info: struct<id:string,public_name:string,organization:string,provider:string,visibility:string,status:string,capabilities:variant,updated_at:timestamp>, context_evaluations: array<struct<id:string,model_a_id:string,model_b_id:string,arena_id:string,arena_slug:string,created_at:timestamp,evaluation_order:int,index:int,messages:array<struct<index:int,user:struct<id:string,parent_message_ids:array<string>,content:array<struct<type:string,text:string,image:string,mimeType:string>>,model_id:string,status:string,created_at:timestamp,message_order:int,modalities:array<string>,token_count:int,index:int>,model_a:struct<id:string,parent_message_ids:array<string>,content:array<struct<type:string,text:string,image:string,mimeType:string>>,model_id:string,status:string,created_at:timestamp,message_order:int,modalities:array<string>,token_count:int,index:int>,model_b:struct<id:string,parent_message_ids:array<string>,content:array<struct<type:string,text:string,image:string,mimeType:string>>,model_id:string,status:string,created_at:timestamp,message_order:int,modalities:array<string>,token_count:int,index:int>>>,input_modalities:array<string>,output_modalities:array<string>,capability_requirements:variant>>, user_token_count: int, user_context_token_count: int, user_language_code: string, model_a_token_count: int, model_a_context_token_count: int, model_a_markdown_elements_count: map<string,bigint>, model_b_token_count: int, model_b_context_token_count: int, model_b_markdown_elements_count: map<string,bigint>, is_coding_conversation: boolean, has_model_refusal: boolean, dedup_tag: struct<high_freq:boolean,hash_count:bigint,sampled:boolean>, creative_writing_v0.1: struct<creative_writing:boolean,score:string>, criteria_v0.1: struct<complexity:boolean,creativity:boolean,domain_knowledge:boolean,problem_solving:boolean,real_world:boolean,specificity:boolean,technical_accuracy:boolean>, if_v0.1: struct<if:boolean,score:int>, math_v0.1: struct<math:boolean>, has_failed_message: boolean, has_flagged_user_message: boolean, is_tie: boolean]


I need to add a new column with the following formula:

`add a column called ttv which is pairwise_feedbacks.created_at - max(pairwise_feedbacks.message_a.created_at, pairwise_feedbacks.message_b.created_at)`