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fffz分析Part6

来自Googology Wiki
Tabelog留言 | 贡献2025年8月30日 (六) 21:42的版本 (文字替换 -“BMS”替换为“BMS”)
(差异) ←上一版本 | 最后版本 (差异) | 下一版本→ (差异)

本词条展示fffz强度分析的第六部分。使用MOCFBMS进行对照

\begin{align}s\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)=\psi(\psi_{I(1,0,0)}(0))=\psi((2~~1-)^{1,0})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)=\mathrm{TBO}\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)=\psi(\psi_{I(1,0,0)}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+1})=\psi(\psi_{I(1,0,0)}(\omega))=\psi((2~~1-)^{1,0})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\omega})=\psi(\psi_{I(1,0,0)}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)=\psi(I(1,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)=\psi(I(1,0,0)+\psi_{I(1,0,0)}(I(1,0,0))\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega+1},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega))=\psi(I(1,0,0)\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(5,2,0)(4,2,1)(5,2,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega+1},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega+1},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)))=\psi(I(1,0,0)\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(5,2,0)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,1)(7,3,0)(6,3,1)(7,3,0)(6,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega+1}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega))=\psi(I(1,0,0)\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\omega\times2}\times\omega)=\psi(I(1,0,0)^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega^2}](\varepsilon_0^{\varepsilon_0\times\omega+\omega^2})=\psi(I(1,0,0)^\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\omega^2})=\psi(I(1,0,0)^\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega^2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega^2}\times\omega)=\psi(I(1,0,0)^{I(1,0,0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega^\omega}\times\omega)=\psi(I(1,0,0)^{I(1,0,0)^{I(1,0,0)}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0})=\psi(\psi_{\Omega_{I(1,0,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\zeta_0)=\psi(\Omega_{I(1,0,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{I(1,0,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega_{\Omega_{I(1,0,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega)](\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_{I(1,0,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+1}))=\psi(\psi_{I_{I(1,0,0)+1}}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\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_{I(1,0,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I(1,0,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I_{I(1,0,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,I(1,0,0)+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega))=\psi(I(2,I(1,0,0)+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega))=\psi(I(3,I(1,0,0)+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega))=\psi(I(\omega,I(1,0,0)+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega))=\psi(I(\Omega,I(1,0,0)+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)\times\omega)=\psi(I(I(1,0,0),1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times2](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times2)\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times2](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times2)\times\omega)=\psi(I(I(1,0,0),2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times3](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times3)\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times3](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega\times3)\times\omega)=\psi(I(I(1,0,0),3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2)](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2))=\psi(I(I(1,0,0),\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2))=\psi(I(I(1,0,0),\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(5,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2)\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega^2)\times\omega)=\psi(\psi_{I(I(1,0,0)+1,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(5,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega\times2}\times\omega))=\psi(I(I(1,0,0)+1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0},\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega^\omega}\times\omega)\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega^\omega}\times\omega)\times\omega)=\psi(I(I(1,0,0)^{I(1,0,0)},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(7,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega))=\psi(\psi_{I(1,0,1)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega))=\psi(I(1,0,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)))=\psi(I(1,0,2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(9,3,0)(8,3,1)(9,3,0)(8,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0})=\psi(I(1,0,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+1})=\psi(I(1,0,\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+\omega})=\psi(I(1,0,\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+\omega}\times\omega)=\psi(\psi_{I(1,1,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+\omega\times2}\times\omega)=\psi(I(1,1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,1,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times2})=\psi(I(1,1,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times2+\omega}\times\omega)=\psi(\psi_{I(1,2,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times2+\omega\times2}\times\omega)=\psi(I(1,2,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times3+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times3+\omega\times2}\times\omega)=\psi(I(1,3,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times4+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\varepsilon_0\times4+\omega\times2}\times\omega)=\psi(I(1,4,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times2}](\varepsilon_0^{\varepsilon_0\times\omega\times2})=\psi(I(1,\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega\times2})=\psi(I(1,\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega\times2}\times\omega)=\psi(\psi_{I(2,0,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega}\times\omega)=\psi(I(2,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times2+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega}\times\omega))=\psi(I(2,0,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,2,1)(6,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega\times2}\times\omega)=\psi(I(2,1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega\times3}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega\times2+\omega\times3}\times\omega)=\psi(I(2,2,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega\times3+\omega}\times\omega)=\psi(I(3,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega\times4+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega\times4+\omega}\times\omega)=\psi(I(4,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2}](\varepsilon_0^{\varepsilon_0\times\omega^2})=\psi(I(\omega,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega^2})=\psi(I(\Omega,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2}+\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2}+\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)=\psi(I(I(1,0,0),0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2}\times2+\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2}\times2+\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega)=\psi(I(I(I(1,0,0),0,0),0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2}\times\omega)=\psi(\psi_{I(1,0,0,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2+\omega}\times\omega)=\psi(I(1,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2+\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2+\omega}\times\omega))=\psi(I(1,0,0,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2+\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2+\varepsilon_0+\omega\times2}\times\omega)=\psi(I(1,0,1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2+\varepsilon_0\times\omega+\omega}](\varepsilon_0^{\varepsilon_0\times\omega^2+\varepsilon_0\times\omega+\omega}\times\omega)=\psi(I(1,1,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2\times2+\omega}\times\omega)=\psi(I(2,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2\times3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2\times3+\omega}\times\omega)=\psi(I(3,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^3}](\varepsilon_0^{\varepsilon_0\times\omega^3})=\psi(I(\omega,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega^3})=\psi(I(\Omega,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^3+\omega}\times\omega)=\psi(I(1,0,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^4+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^4+\omega}\times\omega)=\psi(I(1,0,0,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^5+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^5+\omega}\times\omega)=\psi(I(1,0,0,0,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(3,1,0)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^\omega}](\varepsilon_0^{\varepsilon_0\times\omega^\omega})=\psi(I(1@\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega^\omega})=\psi(I(1@\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega^{\omega^\omega}+\omega}\times\omega)=\psi(I(1@(1,0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,1,0)(5,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\LARGE\color{red}{\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\varepsilon_0^{\varepsilon_0^2})=\psi(\psi_{\Omega_{M+1}}(0))=\psi((1-)^{(1,0)}~~~\rm aft~~~2-2)=SRO}\end{align}

\begin{align}s\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\varepsilon_0^{\varepsilon_0^2})=\psi(\psi_{\Omega_{M+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\varepsilon_1)=\psi(\Omega_{M+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z(\varepsilon_0))=\psi(\Omega_{M+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z(\varepsilon_0^2))=\psi(\Omega_{M+\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{\Omega_{M+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{\Omega_{M+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z(\varepsilon_0^{\varepsilon_0}))=\psi(I_{M+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0+\varepsilon_0\times\omega}\times\omega))=\psi(I(1,M+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega+\omega}\times\omega))=\psi(I(1,0,M+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega^2+\omega}\times\omega))=\psi(I(1,0,0,M+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^\omega+\omega}](\varepsilon_0^{\varepsilon_0\times\omega^\omega+\omega}))=\psi(I(1@\omega,M+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega^{\omega^\omega}+\omega}](\varepsilon_0^{\varepsilon_0\times\omega^{\omega^\omega}+\omega}))=\psi(I(1@(1,0),M+1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\varepsilon_0^{\varepsilon_0^2}))=\psi(\psi_{\Omega_{M_2+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\varepsilon_0^{\varepsilon_0^2})))=\psi(\psi_{\Omega_{M_3+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(9,3,0)(8,4,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2}](\varepsilon_0^{\varepsilon_0^2}))))=\psi(\psi_{\Omega_{M_4+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(9,3,0)(8,4,1)(9,4,1)(10,4,1)(10,4,0)(11,5,0)\\&\large\color{red}{\psi_Z(\varepsilon_0^{\varepsilon_0^2})=\psi(M_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\rm SMO}\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2}+\varepsilon_0)=\psi(M_\omega+\Omega_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2}+\varepsilon_0^{\varepsilon_0})=\psi(M_\omega+I_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2}\times2)=\psi(M_\omega\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2}\times\omega](\varepsilon_0^{\varepsilon_0^2}\times\omega)=\psi(M_\omega\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2}\times\omega)=\psi(M_\omega\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2}\times\omega+\varepsilon_0^{\varepsilon_0^2})=\psi(M_\omega^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2}\times\omega^\omega+\varepsilon_0^{\varepsilon_0^2})=\psi(M_\omega^{M_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,0)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+1})=\psi(M_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+2})=\psi(M_{\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\omega}](\varepsilon_0^{\varepsilon_0^2+\omega})=\psi(M_{\omega^\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\omega})=\psi(M_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0)=\psi(M_{\Omega_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(M_{I_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0^{\varepsilon_0+\omega})=\psi(M_{I_\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0)=\psi(M_{I_{\Omega_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0^{\varepsilon_0^2})=\psi(M_{M_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\omega}\times2+\varepsilon_0^{\varepsilon_0^2})=\psi(M_{M_{M_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2+\omega}\times\omega)=\psi(\psi_{M(1,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0^2+\omega\times2}\times\omega)=\psi(M(1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times2}](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times2})=\psi(\psi_{\Omega_{M(1,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0^2+\omega\times2}\times\omega))=\psi(M(1,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,1)(5,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times2})=\psi(M(1,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times3})=\psi(M(2,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times4})=\psi(M(3,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega}](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega})=\psi(M(\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega})=\psi(M(\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0^2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0^2+\omega\times2}\times\omega)=\psi(M(M(1,0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega+\omega}\times\omega)=\psi(M(1,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega+\varepsilon_0})=\psi(M(1,0,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega+\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega+\varepsilon_0+\omega\times2}\times\omega)=\psi(M(1,1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega\times2}\times\omega)=\psi(M(2,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^2+\omega}\times\omega)=\psi(M(1,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^3+\omega}\times\omega)=\psi(M(1,0,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^\omega}](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^\omega})=\psi(M(1@\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^{\omega^\omega}+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^{\omega^\omega}+\omega}\times\omega)=\psi(M(1@(1,0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,1,0)(5,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^{\omega^{\omega^\omega}}+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2+\varepsilon_0\times\omega^{\omega^{\omega^\omega}}+\omega}\times\omega)=\psi(M(1;0)^{M(1;0)^{M(1;0)^{M(1;0)}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,1,0)(5,1,0)(6,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2}](\varepsilon_0^{\varepsilon_0^2\times2})=\psi(\psi_{\Omega_{M(1;0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2}](\varepsilon_0^{\varepsilon_0^2\times2}))=\psi(\psi_{\Omega_{M(1;1)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times2})=\psi(M(1;\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times2+\omega})=\psi(M(1;\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times2+\omega}+\varepsilon_0^{\varepsilon_0^2})=\psi(M(1;M_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times2+\omega}\times\omega)=\psi(\psi_{M(1;1,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0^2\times2+\omega\times2}\times\omega)=\psi(M(1;1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0}](\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0})=\psi(M(1;1,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega+\omega}\times\omega)=\psi(M(1;1,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega^2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega^2+\omega}\times\omega)=\psi(M(1;1,0,0,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega^\omega}\times\omega)=\psi(M(1;1@\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega^{\omega^\omega}+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times2+\varepsilon_0\times\omega^{\omega^\omega}+\omega}\times\omega)=\psi(M(1;1@(1,0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,1,0)(5,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times3}](\varepsilon_0^{\varepsilon_0^2\times3})=\psi(\psi_{\Omega_{M(2;0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times3})=\psi(M(2;\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times4})=\psi(M(3;\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times5})=\psi(M(4;\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times\omega}](\varepsilon_0^{\varepsilon_0^2\times\omega})=\psi(M(\omega;0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,0,0)\end{align}

\begin{align}s\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times\omega})=\psi(M(\Omega;0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times\omega}+\varepsilon_0^{\varepsilon_0^2})=\psi(M(M_\omega;0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^2\times\omega}\times2+\varepsilon_0^{\varepsilon_0^2})=\psi(M(M(M_\omega;0);0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times\omega}\times\omega)=\psi(\psi_{M(1,0;0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times\omega+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times\omega+\omega}\times\omega)=\psi(M(1,0;0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times\omega^2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times\omega^2+\omega}\times\omega)=\psi(M(1,0,0;0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times\omega^3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times\omega^3+\omega}\times\omega)=\psi(M(1,0,0,0;0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(3,1,0)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times\omega^\omega}\times\omega)=\psi(M(1@\omega;0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^2\times\omega^{\omega^\omega}+\omega}\times\omega](\varepsilon_0^{\varepsilon_0^2\times\omega^{\omega^\omega}+\omega}\times\omega)=\psi(M(1@(1,0);0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(4,1,0)(5,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^3}](\varepsilon_0^{\varepsilon_0^3})=\psi(\psi_{\Omega_{N+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^3}](\psi_Z[\varepsilon_0^{\varepsilon_0^3}](\varepsilon_0^{\varepsilon_0^3}))=\psi(\psi_{\Omega_{N_2+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,1)(6,2,0)(7,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^3}](\psi_Z[\varepsilon_0^{\varepsilon_0^3}](\psi_Z[\varepsilon_0^{\varepsilon_0^3}](\varepsilon_0^{\varepsilon_0^3})))=\psi(\psi_{\Omega_{N_3+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(9,3,1)(9,3,0)(10,4,0)\\&\LARGE\color{red}{\psi_Z(\varepsilon_0^{\varepsilon_0^3})=\psi(N_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)=\rm SNO} \psi_Z(\varepsilon_0^{\varepsilon_0^3+1})=\psi(N_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega})=\psi(N_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0)=\psi(N_{\Omega_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(N_{I_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0+\omega})=\psi(N_{I_\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0)=\psi(N_{I_{\Omega_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0^2})=\psi(N_{M_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0^2+\omega})=\psi(N_{M_\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0)=\psi(N_{M_{\Omega_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(N_{M_{I_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^3+\omega}+\varepsilon_0^{\varepsilon_0^2+\omega}+\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0)=\psi(N_{M_{I_{\Omega_\omega}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^4}](\varepsilon_0^{\varepsilon_0^4})=\psi((1-)^{(1,0)}~~\mathrm{aft}~~(2-2-2-2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(3,1,0)(4,2,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^4})=\psi(1-2-2-2-2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0^5}](\varepsilon_0^{\varepsilon_0^5})=\psi((1-)^{(1,0)}~~\mathrm{aft}~~(2-2-2-2-2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(3,1,1)(3,1,0)(4,2,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^5})=\psi(1-2-2-2-2-2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)(3,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0^{16843009}})=\psi(1-(2-)^{16843009})=(0,0,0)(1,1,1)(2,1,1)\underbrace{(3,1,1)(3,1,1)...(3,1,1)}_{16843009~\rm times} \\&\LARGE\color{purple}{\psi_Z[\varepsilon_0^{\varepsilon_0^\omega}](\varepsilon_0^{\varepsilon_0^\omega})=\psi((2-)^\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,0,0)}\end{align}