I copy this from the novel
If you're curious what meaning after they hug
Sanagi kept crying in his arms. For all that came before, and all that would follow.
Eventually, Sanagi stopped crying and fell asleep in Kousaka's arms.
It was an incredibly deep sleep.
It was the first time in her life she'd had such a peaceful sleep.
In her dream, she was a swan. A swan swimming lonesomely in a lake glittering in the sun during the spring. Her wing was injured, so she'd been left behind by the others. What am I going to do now? The swan couldn't bear the unease. She felt bitter toward the others who had left her behind, and at the same time thought nostalgically of them. And she cursed her lack of caution that caused her precious wings to be injured
But as she swam in the lake upon which cherry petals fell, things gradually stopped mattering. Well, in the end, at least I'm able to have this beautiful sight all to myself, thought the swan.
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I search google about swan
In Japan, white swans are symbols of beauty, grace and love and often feature in the wedding processions of the aristocracy. The swan is also a symbol of prosperity and joy.