Formatting multidimensional array data days wise

Hi I have data response for few days in day sorting order like

Array
(
    [0] => stdClass Object
        (
            [start_time] => 13:00:00
            [end_time] => 13:20:00
            [date] => 2020-08-30
            [day] => sun
        )

    [1] => stdClass Object
        (
            [start_time] => 14:40:00
            [end_time] => 15:00:00
            [date] => 2020-08-30
            [day] => sun 
        )

    [2] => stdClass Object
        (
            [start_time] => 10:00:00
            [end_time] => 10:20:00
            [date] => 2020-08-30
            [day] => mon
        )

    [3] => stdClass Object
        (
            [start_time] => 16:00:00
            [end_time] => 16:20:00
            [date] => 2020-08-30
            [day] => mon
        )

    [4] => stdClass Object
        (
            [start_time] => 15:40:00
            [end_time] => 16:00:00
            [date] => 2020-08-30
            [day] => tue
        )

    [5] => stdClass Object
        (
            [start_time] => 15:20:00
            [end_time] => 15:40:00
            [date] => 2020-08-30
            [day] => tue
        )
)

and I want reformat array in day wise like

Array
(
    [0] => stdClass Object
    (
        [sun] => stdClass Object
        (
            [start_time] => 13:00:00
            [end_time] => 13:20:00
            [date] => 2020-08-30
            [day] => sun
        )
    
        [mon] => stdClass Object
        (
            [start_time] => 10:00:00
            [end_time] => 10:20:00
            [date] => 2020-08-30
            [day] => mon
        )
        
        [tue] => stdClass Object
        (
            [start_time] => 15:40:00
            [end_time] => 16:00:00
            [date] => 2020-08-30
            [day] => tue
        )
    )
    
    [1] => stdClass Object
    (
        [sun] => stdClass Object
        (
            [start_time] => 14:40:00
            [end_time] => 15:00:00
            [date] => 2020-08-30
            [day] => sun 
        )
    
        [mon] => stdClass Object
        (
            [start_time] => 16:00:00
            [end_time] => 16:20:00
            [date] => 2020-08-30
            [day] => mon
        )
        
        [tue] => stdClass Object
        (
            [start_time] => 15:20:00
            [end_time] => 15:40:00
            [date] => 2020-08-30
            [day] => tue
        )
    )
)

for this I code as

foreach ($data as $key => $value) {
    foreach ($week_days as $key1 => $v) {
        $i = 0;
        $response[$key][$v]['start_time'] = $value->start_time;
        $response[$key][$v]['end_time'] = $value->end_time;
        $response[$key][$v]['date'] = $value->date;
        $response[$key][$v]['day'] = $value->day;
        $response[$key][$v]['have_appointment'] = $value->have_appointment;
        $response[$key][$v]['patient_name'] = $value->patient_name;
        $response[$key][$v]['complain'] = $value->complain;
        $i++;
    }
}

but seems it overwrite data & I could not catch where I am making mistake

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