One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the field deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus " very strongly" hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is

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... rily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.