How to know the size of a system evaluation in the nix store?

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1 
sys="$(nix eval --raw "${LOCAL_CONFIG_PATH}#nixosConfigurations.${hostname}.config.system.build.toplevel")"
nix build "${LOCAL_CONFIG_PATH}#nixosConfigurations.${hostname}.config.system.build.toplevel" --out-link "$(mktemp -d)/result" |& nom
nix copy --to "ssh://$dest?remote-store=local?root=/mnt" "$sys" |& nom

Is there a way to know the size of the nix store that will be copied in the 3rd step?

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nix path-info -Sh "$sys" will get you an upper limit of the amount that will be copied. If parts of the closure exist in the remote store, the actual amount copied will be less.