How to filter out a key from a second level object of a nested array of objects

I am trying to filter out a key, in this case, count from a nested array of objects.

I have

let test  = [
 {
  "id": "c3c6f410f58e5836431b473ebcf134756232d04f2bf35edff8",
  "label": "Sector2",
  "options": {
   "62f92fab79ac81d933765bd0bbc4a1f5ea26cb3a088bcb4e6e": {
    "index": 0,
    "value": "Bob",
    "label": "Bob",
    "count": 1
   },
   "2fe91aa3567c0d04c521dcd2fc7e40d7622bb8c3f594d503da": {
    "index": 1,
    "value": "Student",
    "label": "Student",
    "count": 1
   },
   "c59ea1159f33b91a7f6edc6925be5e373fc543e4": {
    "index": 2,
    "value": "BBB",
    "label": "BBB",
    "count": 1
   },
   "c59ea1159f33b91a7f6edc6925be5e373fc54AAA": {
    "index": 3,
    "value": "Orange Duck",
    "label": "Orange Duck",
    "count": 1
   }
  }
 },
 {
  "id": "f794c6a52e793ee6f5c42cd5df6b4435236e3495e951709485",
  "label": "Brown Cow"
 },
 {
  "id": "f794c6a52e793ee6f5c42cd5df6b4435236e3495e95170ZZZ",
  "label": "Red Fish"
 }
]

 test = test.filter(item => item[0].options['count']);

but I am getting Cannot read properties of undefined

I am trying to filter out count from all elements of test that have options

desired output is

Thanks

[
 {
  "id": "c3c6f410f58e5836431b473ebcf134756232d04f2bf35edff8",
  "label": "Sector2",
  "options": {
   "62f92fab79ac81d933765bd0bbc4a1f5ea26cb3a088bcb4e6e": {
    "index": 0,
    "value": "Bob",
    "label": "Bob"
   },
   "2fe91aa3567c0d04c521dcd2fc7e40d7622bb8c3f594d503da": {
    "index": 1,
    "value": "Student",
    "label": "Student"
   },
   "c59ea1159f33b91a7f6edc6925be5e373fc543e4": {
    "index": 2,
    "value": "BBB",
    "label": "BBB",
    "count": 1
   },
   "c59ea1159f33b91a7f6edc6925be5e373fc54AAA": {
    "index": 3,
    "value": "Orange Duck",
    "label": "Orange Duck"
   }
  }
 },
 {
  "id": "f794c6a52e793ee6f5c42cd5df6b4435236e3495e951709485",
  "label": "Brown Cow"
 },
 {
  "id": "f794c6a52e793ee6f5c42cd5df6b4435236e3495e95170ZZZ",
  "label": "Red Fish"
 }
]