"Did use to be" or "did used to be"?

Hi all.

Subject says it all, really.
If you want to query someone whether it commonly was as cold as it is
now, would
"Did it use to be this cold?" or "Did it used to be this cold?" be
correct?

The last version seems obvious, but the "did ... used" jars me, as it
twice uses the past form. However, "did ... use" looks decidedly odd.

Googling for the two terms give "used" 1480 hits vs. "use" 106 hits...
:-)

Any authoritative references on this?

Thanks for your help.

Kind regards,

Morten

.

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