OSPF default-information originate

Hi.
A router has two static default routes to internet pointing to two different gateways.
I wish to have OSPF redistributing a default-route only to one default gateway: if the interface pointing to it goes down, no default-route has to be redistributed.

I’ve configured the router in a similar way:

ip route 0.0.0.0 0.0.0.0 1.1.1.1
ip route 0.0.0.0 0.0.0.0 2.2.2.2

router ospf 1
default-information originate route-map DEFAULT-ROUTE

route-map DEFAULT-ROUTE
match ip next-hop Default-Route

ip access-list standard Default-Route
permit 1.1.1.1

However the default-route doesn’t show up in the neighbor’s routing table.
Does anybody can give me some advice?
Thank you

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