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Steady state number of the short-period(SP) comets captured from nearly parabolic(NP) orbits with 60°≤ i(inclination) ≤ 120° and 0.5≤q (perihelion distance) ≤1.5 AU is calculated. Due to smallness of the q and slowness of the capture process, almost all these SP comets become completely extinct. Combining annual flux of the observed NP comets of high inclination with the capture probability from NP to SP orbits and the ejection rate in SP orbits obtained by Monte Carlo simulations, we find that the steady state number of the extinct SP comets in high-inclination orbits is at least 1-2 hundred. If this number can be considered to correspond to the observed one of Apollo-type objects with i ≥ 60°, it is concluded that only less than a few percent of extinct comets leaves sizable non-volatile cores or shells. The number of asteroid-like bodies deduced from the extinct comets with small perihelion distance and high inclination has less ambiguity than that of low inclination, because contribution from asteroid belt is negligible and the source comets are visible(free from observational selection) through the whole course of orbital evolution.