MongoDB query to get count of array values for specific groups - mongodb

Question

I am trying to achieve a group which tells me the count of occurrence of color and the entity count corresponding to each color.
I have written a query, But this is giving me twice the count because of unwind i guess.
My Query :
db.message.aggregate([
{$unwind: '$entities'},
{ "$group": {
"_id": {
"color": "$color",
"entities" :"$entities"
},
"count": { "$sum": 1 }
}},
{ "$group": {
"_id": "$_id.color",
"count": { "$sum": "$count" },
"entities": {
"$push": {
"entity": "$_id.entities",
"count": "$count"
},
}
}}
])
Database Message Data :
{
"_id" : ObjectId("5c55f99abf6dc481ccfa7f67"),
"color" : "Red",
"channel" : "google",
"content" : "red color",
"entities" : [
"a",
"b"
]
},
{
"_id" : ObjectId("5c57f0a0bf6dc44424e8d371"),
"color" : "Red",
"channel" : "google",
"content" : "red color",
"entities" : [
"a",
"b"
]
},{
"_id" : ObjectId("5c5947a4bf6dc462603d87da"),
"color" : "Blue",
"channel" : "google",
"content" : "yo yo",
"entities" : [
"a",
"b"
]
},
{
"_id" : ObjectId("5c6151b9bf6dc4bee8dac8c9"),
"color" : "Blue",
"handle" : "IBM",
"channel" : "twitter",
"content" : "yo yo",
"entities" : [
"a",
"b",
"c"
]
}
(EDITED) I am Expecting the following Output :
{
"color" : "Red",
"count" : 2,
"entities" : [
{
"entity" : "a",
"count" : 2
},
{
"entity" : "b",
"count" : 2
}
]
},
{
"color" : "Blue",
"count" : 2,
"entities" : [
{
"entity" : "c",
"count" : 1
},
{
"entity" : "b",
"count" : 2
},
{
"entity" : "a",
"count" : 2
}
]
}
Please Help!.