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Map add to list in map:
for (Detail_Prestation__c dp : lstDps) {
// Map of Dates to List of Detail_prestation__c
if (mapDatesToDps.containsKey(dp.Date__c)) {
mapDatesToDps.get(dp.Date__c).add(dp);
} else {
mapDatesToDps.put(dp.Date__c, new List<Detail_prestation__c>{ dp });
}