index,match, mmult, Fomula not working properly

see attachtment.
i have data that looks like this
a b c d e f g
1 1000 2 3 5 449
2 1001 91 92 93 94 95 43
3 1001 96
4 1002 97 98 99 100 101
5 1002 97 98 99 100 101
6 1001 102 104 417
the formula in column a is
=IFERROR(INDEX($A$2:$A2,MATCH(1,MMULT(--($B$2:$H2=$B3),TRANSPOSE(COLUMN($B$2:$H2)^0)),0)),IFERROR(INDEX($A$2:$A2,MATCH(1,MMULT(--($B$2:$H2=$C3),TRANSPOSE(COLUMN($B$2:$H2)^0)),0)),IFERROR(INDEX($A$2:$A2,MATCH(1,MMULT(--($B$2:$H2=$D3),TRANSPOSE(COLUMN($B$2:$H2)^0)),0)),IFERROR(INDEX($A$2:$A2,MATCH(1,MMULT(--($B$2:$H2=$E3),TRANSPOSE(COLUMN($B$2:$H2)^0)),0)),IFERROR(INDEX($A$2:$A2,MATCH(1,MMULT(--($B$2:$H2=$F3),TRANSPOSE(COLUMN($B$2:$H2)^0)),0)),IFERROR(INDEX($A$2:$A2,MATCH(1,MMULT(--($B$2:$H2=$G3),TRANSPOSE(COLUMN($B$2:$H2)^0)),0)),MAX(A$2:A2)+1))))))

i have random data in columns b-h. my goal is to find any overlapping data. as i insert new row of data in column b-h, i am trying to find rows above it sharing any of the numbers and if it finds one above it it should share the same "ID" in column a. if it doesnt find it should insert the next "ID" number. in my example row 3 should automatically update to "1003" being that "96" isnt found in any rows above it. the formula works well as long as there is no data in column g. however as soon as i put data in column g the next row doesnt update properly. what is wrong with my formula.

thanks

Please show in column A manually typed expected results (with an explanation) instead of a non working formula.

Please try in A3 and copy down:

Formula:

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i am trying to find rows above it sharing any of the numbers

Slightly modified the HansDouwe's formula, since it has to cover all the above rows.
In A3

Formula:

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So it is important to provide for a realistic example.

If it is not necessary that the data is in a special order, please provide for such example (including expected results).

thanks for your patience.
attached updated table

Please try in A3 and copy down:

Formula:

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You are Welcome!

Thanks for the feedback and rep. .

Glad to have helped.