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Therefore the Higgs boson couplings need to be measured with a per-cent accuracy or better to be sensitive to 1~TeV new physics, and with a per-mil accuracy to be sensitive to multi-TeV new physics. Similarly, Electroweak precision measurements made at LEP with $10^7$ Z decays, together with accurate W and top-quark mass measurements, were sensitive to weakly-coupled new physics at the TeV scale. To increase this sensitivity up to 10 TeV, an improvement in precision by two orders of magnitude, i.e., an increase in statistics by four orders of magnitude to at least $10^{11}$ Z decays, would be needed. At the same time, the current precision of the W and top-quark mass measurements need to be reduced by at least one order of magnitude, i.e., to better than 1 MeV/$c^2$ and 50 MeV/$c^2$ respectively, in order to match the increased Z-pole measurement sensitivity.   Among the various proposals possibilities  on the table today ($pp$ colliders, $\epem$ colliders, $\mu^+\mu^-$ colliders and $\gamma\gamma$ colliders), it seems that only circular $\epem$ colliders can deliver the integrated luminosities that would be adequate to reach such levels of precision. The proposed TLEP $\epem$ collider~\cite{cite:1305.6498}, which could be hosted in a new 80 to 100 km tunnel~\cite{cite:Osborne} in the Geneva area, as seen in Fig.~\ref{fig:TLEP80}, would be able to produce collisions at centre-of-mass energies between $m_{\rm Z}$ and 500 GeV at several interaction points, and make precision measurements at the Z pole, at the WW threshold, at the HZ cross section maximum, and at the $\ttbar$ threshold, with an unequalled accuracy. This collider also provides a possible upgrade to a hadron collider (called the VHE-LHC) in the same tunnel, at a centre-of-mass energy of up to 100~TeV, which would give direct access to new physics up to scales of 10~TeV or more. This vision is fully in-line with the recent update of the European Strategy, approved at the end of May 2013 by the CERN Council~\cite{cite:Strategy}, which calls upon CERN to develop a proposal for an ambitious post-LHC accelerator project at CERN.