Error saving a new record to Contract?

I am trying to save a new record in Contract,

I have required fields like Account name and Contact name,

Here is part of the code:

         Account[] aa = [SELECT Id, Name FROM Account WHERE Name = :inquery.Institution__c];
          Contact[] ac = [Select AccountId From Contact Where Email =:inquery.email__c];

          contract = new Contract();
          contract.Volume_Serial_Number__c = record.Volume_Serial_Number__c;
          contract.Host_Name__c             = record.Host_Name__c;
          contract.Physical_Address__c      = record.Physical_Address__c;
          contract.License_Type__c          = 'Temporary';
          contract.CustomerSignedId         = ac.get(0).AccountId;
          contract.AccountId                = aa.get(0).Id;
          insert contract;

So the contact and account fields are linked to Contract [look up fields]

When I run the code I get the following error:

Insert failed. First exception on row 0; first error: FIELD_INTEGRITY_EXCEPTION, Institution Contact: id value of incorrect type: 001J0000015XCOKIA4: [CustomerSignedId]

Does anyone know why?

Thanks