Determine if all criteria fit between numerial ranges (for Excel and Google Sheets)

Here is the sample I have created.

Column N is the only column that has input values.
Column K is the result I want.

Column C, E, I is the least acceptable value, column D, G, J is the largest acceptable value.

K2 does not match because item1 is only acceptable at 2, while in columns M/N you see item1 is at 1. The items can repeat!!
K3 also does not match because item3 is only acceptable at values between 1 to 4, while in columns M/N you see item3 at 6.

So on.. All 3 of these critera have to be met in order to return a match as in K5.

Any help here, this seems impossible I've been at it all day... Thanks a lot!