Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this set of alphametic relationships. None of the numbers can contain any leading zero.

**NATE** is divisible by 3, and:
**ATEN** is divisible by 7, and:
**ANTE** is divisible by 11, and:
**NEAT** is divisible by 17.

What are the possible value(s) that

**NEAT** can assume?

40 minutes without computer:

**9027 and 9741**

Without non-distinct digits constraint: **6936** is **ok** as well