aies: subjunctive of avoir (Conjugate avoir in the subjunctive present in French (Le Subjonctif Présent))

Why the subjunctive? Expressing "the most/least that I have (ever)..." with a superlative followed by the subjunctive mood in French (Le Subjonctif)

eue: feminin form of past participle of avoir (Conjugate avoir (+ avoir) in the compound past in French (Le Passé Composé)) which needs to agree in gender with "la meilleure idée" (Special cases when the past participle agrees (in number & gender) when used with 'avoir' in the compound past in French (Le Passé Composé))

Radhika - that is an advanced and complex construct, for sure ! 

Links below to lessons on 

the past subjunctive, 

use of the subjunctive after superlatives, 

agreement of past participle in compound tenses with avoir when the direct object - in this phrase ‘que’ - precedes the verb (passé composé is the exemplar but it applies to all compound tenses conjugated with avoir), 

and of que/qui as object/subject of relative clauses respectively.

These 4 lessons apply to understanding that construction -

 auxiliary avoir in the subjunctive to accord with ‘tu’, 

and past participle of avoir in the plural to agree with the number/gender of the noun that ‘que’ represents. 

The past participle ‘ eue ‘ indicates a grammatically feminine, singular noun replaced by ‘ que ’)

Have also linked to Laura Lawless site on avoir conjugation, and use of the past subjunctive, which is less common than using present subjunctive but still current.

Conjugate verbs in the subjunctive past in French (Le Subjonctif Passé) 

Expressing "the most/least that I have (ever)..." with a superlative followed by the subjunctive mood in French (Le Subjonctif)

 Agreeing past participle with subject's gender and number with (+ être) verbs in the compound past in French (Le Passé Composé)

 Qui = Who/which/that (French Relative Pronouns)

 https://www.lawlessfrench.com/verb-conjugations/avoir/

 https://www.lawlessfrench.com/grammar/past-subjunctive/

Christian and I have responded at same instant !

Merci Christian et Maarten. Very useful answers. Will refer to your comments later when i am ready for this level of complexity.