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Play or Defend 3NT

West
K8743
92
64
10975
North
J652
J6
Q82
AKQ6
East
AQ9
Q1074
A953
J3
South
10
AK853
KJ107
842
W
N
E
S
1
1
P
1
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0

I've taken this hand from one of David Bird's humorous books, making one minor change. 

At the table, South's 3NT contract was defeated: understandably, the text does not give a detailed analysis.  But with both sides double-dummy, do you play or defend?

(If you run the hand through Deep Finesse, or some similar program, please don't post what it says.)

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