update element triple or double nested array element field

//my data
{
    "_id" : ObjectId("57c3d5b3d364e624b4470dfb"),
    "workout" : [
        {
            "workOutId" : "WORK222",
            "exercise" : [
                {
                    "exerciseId" : "EX21",
                    "state" : [
                        {
                            "rep" : "115",
                            "weight" : "400"
                        }
                    ]
                },
                {
                    "exerciseId" : "EX22",
                    "state" : [
                        {
                            "rep" : "120",
                            "weight" : "250"
                        }
                    ]
                }
            ]
        },
        {
            "workOutId" : "WORK123",
            "exercise" : [
                {
                    "exerciseId" : "EX41",
                    "state" : [
                        {
                            "rep" : "150",
                            "weight" : "200"
                        }
                    ]
                },
                {
                    "exerciseId" : "EX55",
                    "state" : [
                        {
                            "rep" : "110",
                            "weight" : "250"
                        }
                    ]
                }
            ]
        }
    ]
}

//change the state[] array element filed where "rep" = 115 and change the "weight" = 600?
//with elemMatch
/* db.getCollection('random').update(
    {
        "workout.exercise.state":{
                    $elemMatch: {
                            "rep": "115"
                        }
            } //query the exact array element
    }, //querry,
    {
        $set: {
                "workout.$[i].exercise.$[j].state.$.weight": "600" //update the value
            }
     }, //update,
    {
        arrayFilters: [
                {
                    "i.workOutId": "WORK222" // querry the workout[] array with the element
                 },
                 {
                    "j.exerciseId": "EX21" //querry the exercise[] array with the element
                  }
            ]
     } //option
)*/

//Without elemMatch with $[<identyfier>]
/*
db.getCollection('random').update(
    {//empty} //querry
    {
        $set: {
                "workout.$[i].exercise.$[j].state.$[k].weight": "500"
            }
     }, //update,
    {
        arrayFilters: [
                {
                    "i.workOutId": "WORK222" //querry the workout[] array
                 },
                 {
                    "j.exerciseId": "EX21" //querry the exercise[] array
                  },
                  {
                    "k.rep": "115" //queery the state[] array
                   }
            ]
     } //option
)
*/

/*update all array filed base on eleMatch*/
/*db.getCollection('random').update(
    {
        "workout.exercise.state": {
              $elemMatch : {
                    rep: "110"
                  }
        },
     },
     {
        $set: {
                "workout.$[].exercise.$[].state.$.weight": "250"
            }
     }
)*/