...

The first two authors have contributed equally to this paper.

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... [Fe/H]

$[X/Y] = \log(X/X_{\odot}) - \log(Y/Y_{\odot}$).

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...(F)

A(Element $) = \log {N}($Element)+12.

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... C+N

We prefer to use C+N rather than C because our models do not take into account the possibility that some C is converted into N.

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... convective

The mixed fraction might be as much as 90% if thermohaline mixing is effective (Stancliffe et al. 2007), even though this may be debated in particular regarding the possible counter-effect of gravitational settling (see, e.g., Aoki et al. 2008; Thompson et al. 2008).

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