各位好
我目前在用MongoDB作資料庫開發系統
有一個語法我百思不得其解不知道該如何作出來

我有一個buyer的collection
裡面有5個buyer資料，並且其聯絡資訊有建一個contact的array
每個buyer的聯絡資料有多也有少(不一定齊全)

我要作的是，撈出這些buyer中，contact資料有任意一組相同的，就要撈出來

以下是我建的collection資料buyer：

{
	"buyer_name" : "Aron",
	"contact" : [ 
		{
			"key" : "cellphone",
			"value" : "0937888444"
		}, 
		{
			"key" : "officephone",
			"value" : "02-25867777"
		}, 
		{
			"key" : "private_email",
			"value" : "test1@gmail.com"
		}
	]
},
{
	"buyer_name" : "Breakgod",
	"contact" : [ 
		{
			"key" : "cellphone",
			"value" : "0937888444"
		}, 
		{
			"key" : "officephone",
			"value" : "02-258666666"
		}, 
		{
			"key" : "public_email",
			"value" : "test21@gmail.com"
		}, 
		{
			"key" : "private_email",
			"value" : "test22@gmail.com"
		}
	]
},
{
	"buyer_name" : "Cindy",
	"contact" : [ 
		{
			"key" : "cellphone",
			"value" : "0937888333"
		}, 
		{
			"key" : "officephone",
			"value" : "02-25862222"
		}, 
		{
			"key" : "private_email",
			"value" : "test3@gmail.com"
		}
	]
},
{
	"buyer_name" : "Dragon",
	"contact" : [ 
		{
			"key" : "cellphone",
			"value" : "0937888222"
		}, 
		{
			"key" : "officephone",
			"value" : "02-25862222"
		}, 
		{
			"key" : "private_email",
			"value" : "test4@gmail.com"
		}
	]
},
{
	"buyer_name" : "Even",
	"contact" : [ 
		{
			"key" : "cellphone",
			"value" : "0937888111"
		},  
		{
			"key" : "private_email",
			"value" : "test5@gmail.com"
		}
	]
}

以下是我下的查詢語法：

db.buyer.aggregate([
 { $lookup:
     {
       from: "buyer",
       let: { id: "$_id", name: "$buyer_name", kk: "$contact.key", vv: "$contact.value"},
       pipeline: [
            { $match:
                { $expr:
                    { $and:
                        [
                           { $eq: [ "$contact.key", "$$kk"] },
                           { $eq: [ "$contact.value", "$$vv"] },
                           { $ne: ["$$id", "$_id" ] }
                        ]
                    }
                }
            }
        ],
        as: "comment"
        }
 }
])

根據我的查詢語法，就會查不出半筆符合的資料
我這語法會將所有contact的資料作key與value的比對
也就因此無法撈出我要的資料了

還請各位高手指點一下
如何可以作到更細部的查詢，使之可以查詢到contact的任意一筆相同的資料就可以符合條件撈出來，謝謝