\[
2\bigl(2(n-1)\bigr) + 2(n-1) = 6(n-1)
\]

\[
\widetilde{P} \xrightarrow{\ (\mathrm{source},\,\mathrm{but})\ } P \times P
\]

\[
\operatorname{Sp}_0(D) \amalg \operatorname{Gn}_0(D),
\]

\[
\widetilde{I} \;\underline{\simeq}\; \text{ens.\ des arêtes de } \widehat{P}(D)
\]

\[
D = \Delta = \Delta_{i_0},
\]

\[
I \smallsetminus \lbrace i_0 \rbrace \;\simeq\; \text{ens.\ des \emph{sommets} de } \widehat{P}(\Delta_{i_0}),
\]

\begin{align*}
\nu_0 &= \text{nb d'arêtes découpées sur la génér.\ } \Delta \text{ par } \Sigma \text{ le long du couloir} \\
&= \text{nb d'arêtes en } D = \ldots n - \nu,
\end{align*}

\[
\nu + \nu_0 = n
\]

\[
\textstyle\sum \text{toutes les pondérations en } D = 2n
\]

\[
\underbrace{\text{Sommets de } \Gamma(\underline{\Sigma})}_{(= \mathrm{Pr}(\Sigma))} \smallsetminus \underbrace{\Sigma}_{\text{p.r.\ supercritiques}} \longrightarrow \begin{array}{c} \text{ens.\ des structures polygonales sur } \widetilde{I} \\ \text{compatibles avec l'antipodisme} \end{array}
\]

\[
\operatorname{Pol}^{*}(D) \to \operatorname{Pol}(D).
\]

\[
\text{pondération de } \widehat{a,x} \text{ dans } \operatorname{Pol}^{*}(D') = \text{somme des pondérations de } \widehat{x,b},\ b,\ \widehat{b,a} \text{ dans } \operatorname{Pol}^{*}(D).
\]

\[
\operatorname{Pol}^{*}(D) \longrightarrow \operatorname{Pol}^{*}(D')
\]

\[
\begin{array}{c} \text{rive des spécialisations} \\ \text{de } D \text{ \uncertain{utilisée}} \end{array} \xrightarrow{\ \sim\ } \mathrm{I}(D', s)
\]

\[
\varphi_{\vec{a}} : \underbrace{\omega(\vec{A}_s)}_{\omega_s} \longrightarrow \underbrace{\omega(\vec{A}_t)}_{\omega_t} \qquad \text{pour } \vec{a} : s \to t
\]

\[
\varphi_{-\vec{a}} = \varphi_{\vec{a}}^{-1}\ ).
\]

\[
\psi_{\vec{a}} : \alpha_{\vec{a}} \xrightarrow{\ \sim\ } \alpha_{-\vec{a}}
\]

\[
\vec{a} \in \vec{A}, \quad \omega \in \underline{\omega}_s \overset{\mathrm{def}}{=} \underline{\omega}(\vec{A}_s),
\]

\[
\left\lbrace
\begin{array}{l}
\rho_f(\vec{a}, \omega_s) = (\vec{b}, \omega_t) \\
\vec{b} = \rho_{\omega_t}^{-1}(-\vec{a})
\end{array}
\right.
\qquad
\begin{array}{l}
\text{où } \omega_t = \varphi_{\vec{a}}(\omega_s) \in \underline{\omega}(A_t) \\
\text{et où } b \in \vec{A}_t \ (t = \operatorname{ex}(\vec{a})) \\
\text{est donné par}
\end{array}
\]

\[
(\Gamma, (\pi_s)_{s \in S}, (\varphi_{\vec{a}})_{\vec{a} \in \vec{A}})
\]

\[
\left\lbrace
\begin{array}{l}
\sigma_0(\vec{a}, \omega_s) = (-\vec{a}, -\varphi_{\vec{a}}\,\omega_s) \\
\sigma_2(\vec{a}, \omega_s) = (\vec{a}, -\omega_s) \\
\sigma_1(\vec{a}, \omega_s) = (\rho_{\omega_s}(a), -\omega_s)
\end{array}
\right.
\]

\[
\operatorname{Rep}(\mathcal{C}) \simeq \coprod_{s \in S} \operatorname{Rep}(\vec{A}_s)
\]

\[
\left\lbrace
\begin{array}{l}
\sigma_0(r) = r', \text{ défini par } \left\lbrace \begin{array}{l} \vec{a}_{r'} = -\vec{a} \\ \omega_{r'} = -\varphi_{\vec{a}}(\omega_r) \end{array} \right. \\
\sigma_1(r) = \widetilde{\sigma}_0(r) \\
\sigma_2(r) = \widetilde{\sigma}_1(r)
\end{array}
\right.
\]

\[
\left\lbrace
\begin{array}{l}
\rho_{\mathrm{som}} = \sigma_2\sigma_1 \ \bigl(= \widetilde{\sigma}_0^{s}\widetilde{\sigma}_1^{s} = \widetilde{\rho}^{s}, \text{ opération de rotation sur les repères d'un polygone comb.}\bigr) \\
\rho_{\mathrm{face}} = \sigma_1\sigma_0
\end{array}
\right.
\]

\[
\rho_f = \sigma_2\sigma_0 \overset{\mathrm{def}}{=} \sigma, \qquad \sigma(\vec{a}, \omega_s) = (-\vec{a}, \varphi_{\vec{a}}\,\omega_s).
\]

\[
\begin{array}{ccc}
\omega(\Delta_L) & \longrightarrow & \omega(\Delta_D) \\
\wr & & \wr \\
\omega(L) & & \omega(D)
\end{array}
\]

\[
\varepsilon(s) = \left\lbrace \begin{array}{ll} +1 & \text{si } s \in L \\ 0 & \text{si } s \notin L \end{array} \right.
\]

\[
\sum_{s \text{ sommet de } F} \bigl(2\nu(s) + \varepsilon(s)\bigr) + \sum_{a \text{ arête de } F} \nu(a)
\]

\[
\mathcal{X} \xrightarrow{\ \varphi\ } X
\]

\[
T_a \overset{\mathrm{def}}{=} (F' \cup F'') \cap T,
\]

\[
S_K = \underbrace{S'_K}_{\text{sommets rouges}} \amalg \underbrace{S''_K}_{\text{sommets noirs}}
\]

\[
\left\lbrace
\begin{array}{ll}
\varepsilon_{F'}(a') = -\varepsilon_F(a) & \text{si } F, F' \text{ sont les deux faces incidentes à } a \\
\varepsilon_F(a) = \varepsilon_F(b) & \text{si } a \text{ et } b \text{ sont adjacentes sur } F, \text{ le sommet commun étant d'ordre } 2 \\
\varepsilon_{a_1}(F_1) = \varepsilon_{a_2}(F_2) & \text{si } F_1 \text{ et } F_2 \text{ sont adjacentes le long d'une arête}
\end{array}
\right.
\]

\[
\sigma_a^F \text{ ou } \sigma_a : \operatorname{Pol}(F) \xrightarrow{\ \sim\ } \operatorname{Pol}(F')
\]

\[
(\nu_{s_1} - 1) + (\nu_{s_2} - 1) + \cdots + (\nu_{s_n} - 1)
\]

\[
\begin{array}{l}
l_s = n - \nu_s \\
l_a = n - 1 - (\nu_s - 1) - (\nu_t - 1) = n - (\nu_s + \nu_t - 1) = (n - \nu_s) - (\nu_t - 1) \\
l_s - l_a = \nu_t - 1 \\
\chi_{2n}(s) = \sum (\nu(s) - 1) = n - 1
\end{array}
\]

\[
\lambda(t) = \widetilde{\rho}_p(t) = (-1)^p (t - \chi_p) \qquad \text{ici } p = 2n \text{ donc } (-1)^p = +1
\]

\[
\lambda(t) = t - \chi_{2n} = t - (n - 1)
\]

\[
\rho_p(t) = \sigma_{p-1} \cdots \sigma_0 (t) = (-1)^p (t - \chi_p)
\]

\[
\begin{array}{ccc}
\operatorname{P}(F_n) & \xrightarrow{\ \sigma_{a_n}\ } & \operatorname{P}(F_{n+1}) \\
\varphi_n \ \wr & & \wr\ \varphi_{n+1} \\
\mathbb{Z}/N\mathbb{Z} & \xrightarrow{\ \sigma_n\ } & \mathbb{Z}/N\mathbb{Z}
\end{array}
\qquad s_{n+1} \longmapsto s_{n+1}
\]

\[
\sigma_n(t) = l_n - t
\]

\[
\begin{array}{ll}
\sigma_0(t) = l_0 - t & \\
\sigma_1(t) = l_1 - t & \sigma_1\sigma_0(t) = l_1 - (l_0 - t) = l_1 - l_0 + t \\
\sigma_2(t) = l_2 - t & \sigma_2\sigma_1\sigma_0(t) = l_2 - l_1 + l_0 - t
\end{array}
\]

\[
\underbrace{(\sigma_n \sigma_{n-1} \cdots \sigma_0)}_{\rho_{n+1}}(t) = l_n - l_{n-1} \cdots + (-1)^n l_0 + (-1)^{n+1} t = (-1)^n (\chi_{n+1} - t) = (-1)^{n+1}(t - \chi_{n+1})
\]

\[
\text{où } \chi_{n+1} = \underbrace{l_0 - l_1 + \cdots + (-1)^n l_n}_{n+1 \text{ termes}}
\]

\[
\nu(n-1) + \nu(n-3) = 2\nu n - 4\nu = 2\nu(n-2)
\]

\[
\boxed{\lambda(t) = t - (n-1)}
\]

\[
\pi_1(\mathcal{X}) \longrightarrow \mathbb{D}_{2n}
\]

\[
\pi_1(\widetilde{\mathcal{X}}) \longrightarrow \mathbb{D}_{2n}
\]

\[
t \longmapsto \lambda'(t) = t - 2(n-1).
\]

\[
\mathbb{D}_{2n} \xrightarrow{\ \chi\ } \pm 1
\]

\[
\begin{array}{l}
2(\text{nb de sommets : balayage}) \\
\quad + 2(\text{nb de droites par-dessus lesquelles balayage}) \\
\quad + 1 \ (\text{décollage}) + 1 \ (\text{atterrissage})
\end{array}
\]

\[
\pi_1(\widetilde{\mathcal{X}}) \longrightarrow \pm 1
\]

\[
\operatorname{Pol}(c) : \operatorname{Pol}(F) \longrightarrow \operatorname{Pol}(F'),
\]

\[
\underline{\omega}_{\ast}(c) : \underline{\omega}(F) \simeq \underline{\omega}(D) \longrightarrow \underline{\omega}(F') \simeq \underline{\omega}(D')
\]

\[
\pi_1(\mathcal{X}, F_D) \longrightarrow \underset{\simeq \mathbb{D}_{2n}}{\operatorname{Aut}(\operatorname{Pol}(D))} \xrightarrow{\ \text{effet sur orientation}\ } \pm 1
\]

\[
\chi_{\ast} : \pi_1(\mathcal{X}, F_D) \longrightarrow \pm 1
\]

\[
\begin{array}{l}
\varepsilon_s(F) = \varepsilon_s(D) = \text{un des deux } n\text{-gones inscrits dans } \operatorname{Pol}(D) = \operatorname{Pol}(F) \\
\varepsilon_a(F) = \varepsilon_a(F) = \text{un des deux } n\text{-gones circonscrits dans } \operatorname{Pol}(D) = \operatorname{Pol}(F)
\end{array}
\]

\[
F = F_D \longrightarrow F_{D'} = F'
\]

\[
\begin{array}{ccc}
\omega(F_D) & \xrightarrow[\text{cond.\ via les } \operatorname{Pol}(D)]{\alpha \ \text{transport parallèle}} & \omega(F_{D'}) \\
\wr & & \wr \\
\omega(F) & \xrightarrow[\text{l'orientation sur } \mathcal{X}]{\beta \ \text{transport de}} & \omega(F') \\
\wr & & \wr \\
\omega(D) & \xrightarrow{\alpha' \ \text{transport parallèle}} & \omega(D')
\end{array}
\]

\[
\alpha = \alpha' \qquad \beta = \alpha\alpha' \ \text{ssi nb de } \struck{\text{points}}\ \text{\uncertain{sing.}}\ N \text{ est pair}
\]

\[
\begin{array}{ccc}
\underline{\omega}(F) \simeq \underline{\omega}(D) & \xrightarrow{\ \underline{\omega}_{\ast}(c)\ } & \underline{\omega}(F') \simeq \underline{\omega}(D') \\[4pt]
\varepsilon_s(F) = \varepsilon_s(D) & \longrightarrow & \varepsilon_s(F') \simeq \varepsilon_s(D') \\[4pt]
\varepsilon_a(F) \simeq \varepsilon_a(D) & \longrightarrow & \varepsilon_a(F') \simeq \varepsilon_a(D')
\end{array}
\]

\[
\underline{\omega}(F) \simeq \varepsilon_s(F) \wedge \varepsilon_a(F)
\]

\[
\boxed{\chi_{\ast}(F) = \chi_s(F)\,\chi_a(F)}
\]

\[
\begin{array}{c}
\| \\
\chi_{\ast}(D) = \chi_s(D)\,\chi_a(D) \\
\| \\
\underline{\omega}(D)
\end{array}
\]

\[
\chi_{\ast}(F)\,\rho_s(F)\,\chi_a(F) = 1.
\]

\[
\underline{\omega}_{\mathcal{X}}(c) = \operatorname{par}(c)\,\underline{\omega}_{\ast}(c)
\]

\[
\boxed{\chi_{\mathcal{X}} = \chi_a\,\chi_c}
\]

\[
\chi_{\ast}, \quad \chi_s, \quad \chi_c
\]

\[
\chi_a = \chi_{\ast} \chi_s \quad \text{et surtout} \quad \chi_{\mathcal{X}} = \chi_{\ast} \chi_c.
\]

\[
u : \pi_1(\mathcal{X}, F_D) \longrightarrow \operatorname{Aut}(\operatorname{Pol}(D)),
\]

\[
u(l_{\vec{D}_i}) = \text{translation par } n-1
\]

\[
\chi_{\mathcal{X}}(l_{D_i}) = 1, \quad \chi_s(l_{D_i}) = (-1)^{n-1}
\]

\[
u_D : \pi_1(\mathcal{X}, F_D) \longrightarrow \operatorname{Aut}(F_D)
\]

\[
\text{poids } c \equiv \operatorname{sing}_{D'} - \operatorname{sing}_D \pmod 2
\]

\[
\boxed{\chi_{\mathcal{X}} = \chi_{\ast}}
\]

\[
\omega \text{ or.\ de } \Delta_D \longleftrightarrow \omega_D \text{ or.\ de } D
\]

\[
\omega' \text{ or.\ de } \Delta_{D'} \longleftrightarrow \omega_{D'} \text{ or.\ de } D',
\]

\[
\mathcal{X} \to X,
\]

\[
\sigma_0 \sigma_1 \cdots \sigma_{N-1} \quad \Big| \quad \sigma_N = \sigma_0
\]

\[
\rho_1 = \sigma_0\sigma_1 \quad \rho_2 = \sigma_1\sigma_2 \quad \cdots \quad \rho_N = \sigma_{N-1}\sigma_N = \sigma_{N-1}\sigma_0
\]

\[
\rho_1\rho_2 = \sigma_0\sigma_2 \quad \rho_2\rho_3 =
\]

\[
\begin{array}{ccc} \chi_0 & \chi_1 & \chi_2 \\ 1 & \bar{\varepsilon} & 0 \\ 1 & \xi & 0 \\ 1 & \eta & 1 \end{array}
\qquad
\begin{array}{ccc} 1 & 1 & 0 \\ 1 & \xi & 0 \\ 1 & \eta & 1 \end{array}
\qquad
\begin{array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & \eta & 1 \end{array}
\]

\[
n - \nu - (\nu - 1) - (\nu' - 1) + \nu \;=\; n - (\nu' - 1)
\]

\[
2n - \underbrace{\bigl[ (\nu - 1) + (\nu' - 1) \bigr]}
\]

\[
\pi_1(\mathcal{X}, D) \longrightarrow \mathbb{D}_{2n}
\]

\[
\pi_1(\widetilde{\mathcal{X}}, D) \longrightarrow \operatorname{Aut}\operatorname{Pol}(D) \simeq \mathbb{D}_{2n}
\]

\[
\tau_X = \underline{a}^{\nu} \tau_{\mathcal{X}} ,
\]

\[
\sigma_0\ \sigma_f\ \sigma_1\ \sigma_s\ \sigma_2\ [\sigma_0 \ldots]
\]

\[
2\nu - 2 + (2 + 2) = 2\nu + 2
\]

\[
n - (\nu + \nu' - 1) = (n-1) - (\nu - 1) - (\nu' - 1)
\]

\[
n - \nu - (\nu' - 1)
\]

\[
n - \nu \qquad n - \nu - (\nu' - 1) \qquad n - \nu \qquad n - \nu' \qquad n - \nu' \qquad n - 1 \qquad \nu
\]

\[
n - \nu \qquad 2n - \nu - \nu' + 2 \qquad 2n - (\nu + \nu' - 2) \quad \underline{\varepsilon \geqslant 2}
\]

\[
2n - 2(\nu + \nu' - 1) \qquad 2n - (\nu + \nu' - 1)
\]

\[
\varepsilon = \begin{cases} +1 & \text{si la face spéciale est du type sommet (ultra-\ldots)} \\ -1 & \text{sinon} \end{cases}
\]

\[
N' = N - 1
\]

\[
N' = N
\]

\[
(\mathcal{X}, K, (\delta_s), (\nu_s), (\nu_{\ill{}}))
\]

\[
\begin{array}{ccc}
\omega(D) & \xrightarrow[\text{comb.\ } \beta]{\text{rot } \alpha} & \omega(D') \\
\| & & \| \\
\omega(\mathcal{X}, D) & & \omega(\mathcal{X}, D')
\end{array}
\]

\[
\omega_D \wedge \omega_{D'} \wedge \lbrace D, D' \rbrace \qquad \omega_{D'} \wedge \omega_{D''} \wedge \lbrace D', D'' \rbrace
\]

\[
\rho_D \simeq \omega_{D'} \qquad \rho_{D'} \simeq \omega_D \qquad \rho_D \wedge \omega_{D'} \qquad \rho_{D'} \wedge \omega_D
\]

\[
(n - 2) + (n - 3) = 2n - 5 \qquad 2(n-1)(2n-5) \qquad 2n
\]

\[
\chi(\mathcal{X}) = s_0 - s_1 + s_2 = 1 - g
\]

\[
2 s_1 = \underbrace{4 s_0}_{\sum_{s \in S} \nu_s} = 2 \sum_{f \in F} n_f
\]

\[
\boxed{\sigma_1,\ \sigma,\ \sigma_2,\ \sigma_0}
\]

\[
\frac{\alpha + \gamma + 1}{2} \qquad \frac{\beta + \gamma + 1}{2}
\]

\[
\frac{\alpha + \beta + 2\gamma + 2}{2} \leqslant \alpha + \beta + \gamma + 1 \quad \ill{}
\]

\[
2n \big/ 2(n+1) \qquad 2 \geqslant 2n
\]

\[
\begin{array}{cccccccc}
1 & 2 & 3 & 4 & 1' & 2' & 3' & 4' \\
\xi_0 & \xi_1 & \xi_2 & \xi_3 = \xi_{n-1} & & & &
\end{array}
\]

\[
\widetilde{\Delta}_{\tilde{s}} \xrightarrow[\sim]{\varphi_0} \widetilde{\Delta}'_{\tilde{s}_0}
\qquad
\widetilde{\Delta}_{\tilde{s}} \xrightarrow{\varphi_1} \widetilde{\Delta}^{\ast}_{\tilde{s}_1}
\]

\[
\alpha,\ u^{n}\xi_0,\ u^{n+1}\xi_0,\ \ldots,\ u^{2(n-1)-1}\xi_0
\qquad
\alpha,\ u^{n}\xi_0,\ u^{n+1}\xi_0,\ \ldots,\ u^{2n-2}\xi_0
\]

\[
\xi_0\ \xi_1 \cdots \xi_{n-2}\ \xi_{n-1} = \xi'_0
\qquad
\xi_0\ \xi_1 \cdots \xi_{n-1}\ \xi_n = \xi'_0
\]

\[
\begin{array}{cccc}
1 & 2 & 3 & 4 \\
1' & 2' & 3' & 4'
\end{array}
\qquad
0\ 2'\ 3'\ 4'\ 0'\ 1\ 2\ 3\ 4\ 1'
\]

\[
\begin{array}{ccccc}
\sigma & - & \sigma_2 & - & \sigma_0 \\
\backslash & & & & \\
\sigma_1 & & & &
\end{array}
\]

\[
s_1\ s_2\ s_3\ s_4\ s_5\ s_6 = s_1\ s_2\ t_2\ s_3,\ s_4,\ t_3,\ s_5,\ s_6 = s_1,\ s_2,\ t_2,\ t_3,\ s_4,\ t_3,\ s_5 \quad s_6 = s_1
\]

\[
D_1 \mid D_2\ D_3\ D_4\ D_5\ D_6 \mid D_7\ D_8\ D_9\ D_{10}\ D_{11}\ D_{12}\ D_{13}
\]

\[
\mid D_{14}\ D_{15}\ D_{16}\ D_{17}\ D_{18}\ D_{19}\ D_{20} \overset{?}{=} D_6 \mid
\]

\[
\underbrace{\sigma\sigma'}_{\sigma_1},\ \underbrace{\sigma}_{\sigma},\ \underbrace{\sigma'}_{\sigma_2},\ \underbrace{\sigma'}_{\sigma_0}
\qquad\qquad
\underbrace{\sigma\sigma'}_{\sigma'_0},\ \underbrace{\sigma'}_{\sigma'_1},\ \underbrace{\sigma}_{\sigma'_2}
\]

\[
\frac{1}{2}\,\frac{n(n-1)}{2}\left(\frac{n(n-1)}{2} - 1\right) - \frac{n(n-1)(n-2)}{2} = {}\struck{\ill{}} \sim \frac{1}{8}\,n^4
\]

\[
\begin{array}{ll}
\struck{A\,B\,C\,D\,E\,F\,G} & \\
A\,B\,C\,D\,E\,F\,G \quad \struck{A\,B\,C\,E\,D\,G\,F} & 1' \\
A\,B\,C\,E\,D\,G\,F & 2' \\
A\,B\,C\,E\,G\,D\,F & 3' \\
A\,B\,C\,G\,E\,D\,F & 4' \\
A\,B\,G\,C\,E\,D\,F & 5' \\
A\,G\,B\,C\,E\,D\,F & 6' \\
(A\,G)\,C\,B\,E\,D\,F & 7' \\
(A\,G)\,C\,E\,B\,D\,F & 8' \\
(A\,G)\,E\,C\,D\,B\,F & 9' \\
G\,A\,E\,D\,C\,F\,B &
\end{array}
\]

\[
\sigma_3,\ \sigma_4,\ \sigma_5,\ \sigma_2,\ \sigma_6,\ \sigma_1,\ \sigma_5,\ \sigma_3,\ \sigma_6,\ \ill{},\ \sigma_3\ \sigma_5,\ \sigma_2\ \sigma_6,\ \ill{}
\]

\[
\prod_{s \in S_{D'} \setminus S_D} \mathcal{E}_{D',s}
\]

\[
\begin{array}{ll}
\rho_s = \sigma_2 \sigma_1 & \sigma_1 \\
\rho_f = \sigma_1 \sigma_0 & \sigma_1 = \rho_f^{\,\sigma_0} \\
\rho_s \rho_f = \sigma &
\end{array}
\]

\[
\begin{array}{lcl}
(D_0, \beta^{*}, \omega^{*}) & \overset{\sigma}{\longmapsto} & (D_0, -\beta^{*}, \omega^{*}) \\[2pt]
(D_0, \beta^{*}, \omega^{*}) & \overset{\sigma_0}{\longmapsto} & (D_0, \beta^{*}, -\omega^{*}) \\[2pt]
(D_0, \beta^{*}, \omega^{*}) & \overset{\sigma_2}{\longmapsto} & (D_0, -\beta^{*}, -\omega^{*})
\end{array}
\]

\[
\varphi^{-1}(X_1) = L \cup K_0 \qquad (\text{et } \ill{} = L\,!)
\]

\[
\varepsilon_s = \begin{cases} 0 & s \notin L \\ 1 & s \in L \end{cases}
\]

\[
\sum_{s \in S(K) \cap F} (2\gamma_s + \varepsilon_s) + \sum_{a \in A(K),\ a \subset F} \gamma_a = 2n
\]

\[
1 \xrightarrow{\text{spéc}} 2 \xrightarrow{\text{gén}} 3 \xrightarrow{\text{gén}} 4 \xrightarrow{\text{spéc}} 5 = 1
\]