Substitute each of the capital letters in bold by a different digit from 0 to 9 such that the sum of digits of each of **POIRE**, **OPERA**, **PORTE**, ** TAPIS**, **ASTRE**, **PATRE**, **LOTUS**, **LISTE**, **LOUPE** and, **OUTRE** (in this order) constitutes ten consecutive terms of an arithmetic sequence in ascending order. It is known that none of **P**, **O**, **T**, **A** and **L** can be zero.

OPERA and PORTE are consecutive and share O,P,E,R, so A+1=T

ASTRE and PATRE are consecutive and share A,T,R,E, so S+1=P

LISTE and LOUPE are consecutive, share L and E, so I+S+T+1=O+U+P

with S+1=P then I+T=O+U

LOTUS and LISTE are consecutive and share L,T,E, so O+U+1=I+E

with I+T=O+U, then T+1=E

POIRE and PORTE differ by 2 and share P,O,R,E, so I+2=T

PORTE and OUTRE differ by 7 and share O,R,T,E, so P+7=U

PATRE and LISTE differ by 2 and share T and E, so P+A+R+2=L+I+S

with S+1=P and I+1=A, then R+4=L

Now, S and P are consecutive, P+7=U

I,A,T,E are all consecutibe

and R+4=L

For all those to fit together in ten digits, the order must be one of:

1: O,S,P,R,I,A,T,E,L,U

2: S,P,R,I,A,T,E,L,U,O

3: R,S,P,O,L,I,A,T,E,U

The difference of POIRE and TAPIS should be 3:

1:POIRE=16, TAPIS=18, diff=2: NO

2:POIRE=21, TAPIS=13, diff=-8: NO

3:POIRE=18, TAPIS=21, diff=2: YES

R=0,S=1,P=2,O=3,L=4,I=5,A=6,T=7,E=8,U=9