fffz分析Part4:BIO~JO

本词条展示fffz分析的第四部分。使用 $M O C F$ 和BMS进行分析

\begin{align}s\\&\psi_Z(\varepsilon_0^\omega)=\psi(\Omega_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\varepsilon_0^\omega+\varepsilon_0)=\psi(\Omega_{ \Omega}+\psi_1(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\varepsilon_1)=\psi(\Omega_{\Omega}+\psi_1(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,0)(2,2,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\varepsilon_\omega)=\psi(\Omega_{\Omega}+\psi_1(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,0)(3,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z(\varepsilon_0))=\psi(\Omega_{\Omega}+\psi_1(\Omega_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z(\varepsilon_0^2))=\psi(\Omega_{\Omega}+\psi_1(\Omega_{\omega^2}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z(\varepsilon_0^3))=\psi(\Omega_{\Omega}+\psi_1(\Omega_{\omega^3}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(3,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0,\color{red}{\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega)}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega))=\psi(\Omega_{\Omega}+\psi_1(\Omega_{\omega^\omega}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,0,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega))=\psi(\Omega_{\Omega}+\psi_1(\Omega_{\Omega}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega}\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega}\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega))=\psi(\Omega_{\Omega}\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(3,0,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^\omega\times\omega](\psi_Z(\varepsilon_0)))=\psi(\Omega_{\Omega}\times\psi(\Omega_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(3,1,0)(4,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega))=\psi(\Omega_{\Omega}\times\Omega_2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))=\psi(\psi_\Omega(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,0)(4,3,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1})))^?=\psi(\Omega_{\Omega\times2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,0)(4,3,1)(5,3,1)(6,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))))^?=\psi(\Omega_{\Omega\times3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,0)(4,3,1)(5,3,1)(6,1,0)(5,3,0)(6,4,1)(7,4,1)(8,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^{\omega+1}))=\psi(\Omega_{\Omega\times \omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^{\omega+2}))=\psi(\Omega_{\Omega\times \omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,1)(3,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^{\omega+3}))=\psi(\Omega_{\Omega\times \omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,1)(3,2,1)(3,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^{\omega\times2}))=\psi(\Omega_{\Omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,1)(4,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^{\omega\times3}))=\psi(\Omega_{\Omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,1)(4,1,0)(3,2,1)(4,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^{\omega^2}))=\psi(\Omega_{\Omega^\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(4,1,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\psi_Z(\varepsilon_0)))=\psi(\Omega_{\psi_1(\Omega_\omega)})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(5,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega](\psi_Z[\varepsilon_0^\omega](\psi_Z(\varepsilon_0))))=\psi(\Omega_{\psi_1(\Omega_{\psi_1(\Omega_\omega)})})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(5,2,1)(6,2,1)(7,1,0)(8,2,1)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{\Omega_2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,2,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z(\varepsilon_0^\omega)))=\psi(\Omega_{\Omega_3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,2,0)(2,2,0)(3,3,1)(4,3,1)(5,3,0)\\&\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z[\varepsilon_0^\omega+\varepsilon_0](\psi_Z(\varepsilon_0^\omega))))=\psi(\Omega_{\Omega_4})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,2,0)(2,2,0)(3,3,1)(4,3,1)(5,3,0)(3,3,0)(4,4,1)(5,4,1)(6,4,0)\\&\large\color{red}{\psi_Z(\varepsilon_0^\omega+\varepsilon_0)=\psi(\Omega_{\Omega_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)}\end{align}

\begin{align}s\\&\psi_Z(\varepsilon_0^\omega+\varepsilon_0^2)=\psi(\Omega_{\Omega_{\omega^2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^\omega+\varepsilon_0^3)=\psi(\Omega_{\Omega_{\omega^3}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^\omega\times2](\varepsilon_0^\omega\times2)=\psi(\Omega_{\Omega_{\omega^\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^\omega\times2)=\psi(\Omega_{\Omega_{\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^\omega\times3)=\psi(\Omega_{\Omega_{\Omega_{\Omega}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^\omega\times4)=\psi(\Omega_{\Omega_{\Omega_{\Omega_{\Omega}}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\large\color{purple}{\psi_Z[\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\omega}\times\omega)=\psi(\psi_I(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)=\mathrm{EBO}}\\&\psi_Z[\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\omega}\times\omega+\omega)=\psi(\psi_I(0)+1)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,0)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega,\varepsilon_0^{\omega}\times\omega+\varepsilon_0](\varepsilon_0^{\omega}\times\omega+\varepsilon_0)=\psi(\psi_I(0)+\psi_1(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,0)(2,2,0)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\omega}\times\omega+\varepsilon_0)=\psi(\psi_I(0)+\Omega_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\omega}\times\omega+\varepsilon_0^2)=\psi(\psi_I(0)+\Omega_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\omega}\times\omega+\varepsilon_0^3)=\psi(\psi_I(0)+\Omega_{\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega,\varepsilon_0^{\omega}\times\omega+\varepsilon_0^\omega](\varepsilon_0^{\omega}\times\omega+\varepsilon_0^\omega)=\psi(\psi_I(0)+\Omega_{\omega^\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,0,0)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\omega}\times\omega+\varepsilon_0^\omega)=\psi(\psi_I(0)+\Omega_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\omega}\times\omega+\varepsilon_0^\omega\times2)=\psi(\psi_I(0)+\Omega_{\Omega_{\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\omega}\times\omega)=\psi(\psi_I(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z(\varepsilon_0^{\omega}\times\omega+\varepsilon_0)=\psi(\psi_I(0)\times\Omega_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\omega}\times\omega+\varepsilon_0^\omega)=\psi(\psi_I(0)\times\Omega_\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega}\times\omega\times2](\varepsilon_0^{\omega}\times\omega\times2)=\psi(\psi_I(0)^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\omega}\times\omega\times2)=\psi(\psi_I(0)^\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,1,0)\\&\psi_Z(\varepsilon_0^{\omega}\times\omega^2)=\psi(\psi_I(0)^{\Omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,1,0)(3,1,0)\\&\psi_Z(\varepsilon_0^\omega\times\omega^{\omega})=\psi(\psi_I(0)^{\psi_I(0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^\omega\times\omega^{\omega^\omega})=\psi(\psi_I(0)^{\psi_I(0)^{\psi_I(0)}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,1,0)(4,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1})=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\omega^\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega^\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,0)(2,1,0)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1},\varepsilon_0^{\omega+1}+\varepsilon_0](\varepsilon_0^{\omega+1}+\varepsilon_0)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\psi_1(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,0)(2,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\varepsilon_0)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\varepsilon_0^2)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\varepsilon_0^3)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega_{\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega+1},\varepsilon_0^{\omega+1}+\varepsilon_0^\omega](\varepsilon_0^{\omega+1}+\varepsilon_0^\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega_{\omega^\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\varepsilon_0^\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\varepsilon_0^\omega\times2)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\Omega_{\Omega_{\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1},\varepsilon_0^{\omega+1}+\varepsilon_0^\omega\times\omega](\varepsilon_0^{\omega+1}+\varepsilon_0^\omega\times\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\psi_I(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}+\varepsilon_0^\omega\times\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)+\psi_I(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times2)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times3)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(2,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_1)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(3,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_2)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(3,2,0)(3,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_\omega+\varepsilon_0)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(1,1,1)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_\omega+\varepsilon_0^2)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\omega^2}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(1,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_\omega+\varepsilon_0^\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1},\varepsilon_\omega+\varepsilon_0^\omega\times\omega](\varepsilon_\omega+\varepsilon_0^\omega\times\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\psi_I(0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_\omega+\varepsilon_0^\omega\times\omega)=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\psi_I(0)\times\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_{\omega+1})=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\psi_I(0)+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(3,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_{\omega+2})=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\psi_I(0)+2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(3,2,0)(4,1,0)(3,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_{\omega\times2})=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\psi_I(0)+\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(4,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_{\varepsilon_0})=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\psi_{\Omega_{\psi_I(0)+1}}(0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_{\varepsilon_{\varepsilon_0}})=\psi(\psi_{\Omega_{\psi_I(0)+1}}(\psi_{\Omega_{\psi_I(0)+1}}(\psi_{\Omega_{\psi_I(0)+1}}(0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,1,0)(5,2,0)(6,1,0)(7,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\zeta_0)=\psi(\Omega_{\psi_I(0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z(\varepsilon_0))=\psi(\Omega_{\psi_I(0)+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z(\varepsilon_0^2))=\psi(\Omega_{\psi_I(0)+\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z(\varepsilon_0^3))=\psi(\Omega_{\psi_I(0)+\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(4,2,1)\\&\psi_Z[\varepsilon_0^{\omega+1},\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega)](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega))=\psi(\Omega_{\psi_I(0)+\omega^\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega))=\psi(\Omega_{\psi_I(0)+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times2))=\psi(\Omega_{\psi_I(0)+\Omega_\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times3))=\psi(\Omega_{\psi_I(0)+\Omega_{\Omega_\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega))=\psi(\Omega_{\psi_I(0)\times2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega))=\psi(\Omega_{\psi_I(0)\times\Omega_2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^\omega,\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))=\psi(\Omega_{\psi_{\Omega_{\psi_I(0)+1}}(0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(4,2,1)(5,1,0)(6,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z(\varepsilon_0^{\omega}\times2))=\psi(\Omega_{\Omega_{\psi_I(0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z(\varepsilon_0^{\omega}\times3))=\psi(\Omega_{\Omega_{\Omega_{\psi_I(0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(3,2,1)(4,2,1)(5,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z(\varepsilon_0^{\omega}\times4))=\psi(\Omega_{\Omega_{\Omega_{\Omega_{\psi_I(0)+1}}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(3,2,1)(4,2,1)(5,2,0)(3,2,1)(4,2,1)(5,2,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))=\psi(\psi_I(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1})))=\psi(\psi_I(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,0)(6,0,0)\\&\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))))=\psi(\psi_I(3))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,0)(6,3,0)(7,4,1)(8,4,1)(9,4,0)(8,0,0)\\&\psi_Z(\varepsilon_0^{\omega+1})=\psi(\psi_I(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\omega+2})=\psi(\psi_I(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\omega+3})=\psi(\psi_I(\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega\times2}](\varepsilon_0^{\omega\times2})=\psi(\psi_I(\omega^\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\omega\times2})=\psi(\psi_I(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\omega\times2}+\varepsilon_0)=\psi(\psi_I(\Omega_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\omega\times2}+\varepsilon_0^2)=\psi(\psi_I(\Omega_{\omega^2}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\omega\times2}+\varepsilon_0^\omega)=\psi(\psi_I(\Omega_\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\omega\times2}+\varepsilon_0^\omega\times2)=\psi(\psi_I(\Omega_{\Omega_\Omega}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\omega\times2}\times2)=\psi(\psi_I(\psi_I(\psi_I(\Omega))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)=\psi(I)=\psi(2~~1-2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^2)=\psi(I+\Omega_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^3)=\psi(I+\Omega_{\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^\omega)=\psi(I+\Omega_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega,\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega)=\psi(I+\psi_I(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega)=\psi(I+\psi_I(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^{\omega+1})=\psi(I+\psi_I(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^{\omega+2})=\psi(I+\psi_I(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega,\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^{\omega\times2})=\psi(I+\psi_I(\omega^\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,0,0)\\&\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega+\varepsilon_0^{\omega\times2})=\psi(I+\psi_I(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\omega\times2}\times\omega)=\psi(I+\psi_I(I)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z[\varepsilon_0^{\omega\times2+1},\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega))=\psi(I\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\omega\times2+1},\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\omega\times2+1},\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)))=\psi(I\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,0)(6,3,1)(7,3,0)(6,0,0)\\&\psi_Z[\varepsilon_0^{\omega\times2+1}](\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega))=\psi(I\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z[\varepsilon_0^{\omega\times2+1}](\psi_Z(\varepsilon_0^{\omega\times2}\times\omega))=\psi(I\times\Omega_2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,2,0)(3,2,1)(4,2,0)(3,2,1)(4,2,0)\\&\psi_Z(\varepsilon_0^{\omega\times3}\times\omega)=\psi(I^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\omega\times4}\times\omega)=\psi(I^3)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega^2}](\varepsilon_0^{\omega^2})=\psi(I^\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(3,0,0)\\&\psi_Z(\varepsilon_0^{\omega^2})=\psi(I^\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(3,1,0)\\&\psi_Z[\varepsilon_0^{\omega^2}\times\omega](\varepsilon_0^{\omega^2}\times\omega)=\psi(I^I)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega^\omega}\times\omega](\varepsilon_0^{\omega^\omega}\times\omega)=\psi(I^{I^I})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\omega^{\omega^\omega}}\times\omega](\varepsilon_0^{\omega^{\omega^\omega}}\times\omega)=\psi(I^{I^{I^I}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,1,0)(5,1,0)(2,0,0)\\&\LARGE\color{purple}{\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0})=\psi(\psi_{\Omega_{I+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)=\mathrm{JO}}\end{align}