(CNN) On the night of Donald Trump's inauguration as US President, champagne corks popped in Moscow.

Literally, on the floor of the Russian parliament, MPs cracked open bottles of sparkling wine and toasted his victory.

The thing is, they saw Trump's victory as their victory, too. And why wouldn't they? As presidential candidate, Trump promised to turn US policy towards Russia on its head.

He criticized Russia's Cold War nemesis, NATO, a mainstay of US military power in Europe. He had spoken of working with Russia in Syria, where Moscow supports Bashar al-Assad, whom Washington opposes.

Trump hinted at easing painful sanctions imposed by Washington on Moscow over its intervention in Ukraine, even at recognizing Russian sovereignty over Crimea -- the Ukrainian territory annexed by Russia in 2014.

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