Abstract

Computation lithography is enabled by a combination of physical understanding, mathematical abstraction, and implementation simplification. An application in the virtual world of computation lithography can be a virtual reality or a virtual virtuality depending on its engineering sensible-ness and technical feasibility. Examples under consideration include design-for-manufacturability and inverse lithography.

© 2009 Optical Society of America

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  12. Q3. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, "Massively parallel algorithms for scattering in optical lithography," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 10(9), 1091-1100 (1991).
  13. J. A. Sethian, "Fast marching level set methods for three-dimensional photolithography development," in Proc. SPIE, G. Fuller, ed., vol. 2726, pp. 262-272 (1996).
  14. S. Osher and J. A. Sethian, "Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations," J. Comput. Phys. 79, 12-49 (1988).
  15. J. F. Chen, T. Laidig, K. Wampler, and R. Caldwell, "Optical proximity correction for intermediate-pitch features using sub-resolution scattering bars," J. Vac. Sci. Technol. B 15(6), 2426-2433 (1997).
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  17. N. Cobb and A. Zakhor, "Experimental Results on Optical Proximity Correction with Variable Threshold Resist Model," in Proc. SPIE, G. Fuller, ed., vol. 3051, pp. 458-468 (1997).
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  19. T. Waas, H. Eisenmann, and H. Hartmann, "Proximity Correction for high CD-Accuracy and Process Tolerance," in Proc. Symposium on Nanocircuit Engineering (1994).
  20. H.-Y. Liu, L. Karklin, Y.-T. Wang, and Y. C. Pati, "Application of alternating phase-shifting masks to 140 nm Gate Patterning II: Mask design and manufacturing tolerances," in Proc. SPIE, vol. 3334, pp. 2-14 (1998).
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  22. Q4. Y. C. Pati, A. A. Ghazanfarian, and R. F. Pease, "Exploiting Structure in Fast Aerial Image Computation for Integrated Circuit Patterns," IEEE Trans. Semi. Manufactur. 10(1), 62-74 (1997).
  23. A. E. Rosenbluth, G. Gallatin, R. Gordon, W. Hinsberg, J. Hoffnagle, F. Houle, K. Lai, A. Lvov, M. Sanchez, and N. Seong, "Fast calculation of images for high numerical aperture lithography," in Proc. SPIE, B. Smith, ed., vol. 5377, pp. 615-628 (2004).
  24. M. Born and E. Wolf, Principles of Optics, pp. 491-555, sixth ed. (Pergamon Press, 1980).
  25. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).
  26. A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2001).
  27. A. K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005).
  28. J. Kim and M. Fan, "Hotspot detection on post-OPC layout using full-chip simulation-based verification tool: a case study with aerial image simulation," in Proc. SPIE, K. R. Kimmel and W. Staud, eds., vol. 5256, pp. 919-925 (2003).
  29. S. D. Shang, Y. Granik, N. B. Cobb, W. Maurer, Y. Cui, L. W. Liebmann, J. M. Oberschmidt, R. N. Singh, and B. R. Vampatella, "Failure prediction across process window for robust OPC," in Proc. SPIE, A. Yen, ed., vol. 5040, pp. 431-440 (2003).
  30. H. Mashita, T. Kotani, F. Nakajima, H. Mukai, K. Sato, S. Tanaka, K. Hashimoto, and S. Inoue, "Tool-induced hotspot fixing flow for high volume products," in Proc. SPIE, vol. 7028, p. 70283I (2008).
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  35. S. H. Chan, A. K. Wong, and E. Y. Lam, "Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography," Opt. Express 16, 14,746-14,760 (2008).
  36. A. Poonawala and P. Milanfar, "Mask design for optical microlithography—an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
    [PubMed]
  37. N. Jia, A. K. Wong, and E. Y. Lam, "Robust Photomask Design with Defocus Variation Using Inverse Synthesis," in Proc. SPIE, vol. 7140, p. 71401W (2008).
  38. Q5. E. Y. Lam and J. W. Goodman, "Iterative Statistical Approach to Blind Image Deconvolution," J. Opt. Soc. Am. A 17(7), 1177-1184 (2000).
  39. B. Yenikaya and A. Sezginer, "A rigorous method to determine printability of a target layout," in Proc. SPIE, A. K. K. Wong and V. K. Singh, eds., vol. 6521, p. 652112 (2007).
  40. Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).
  41. W. H. Arnold, "Guest Editorial: Special Section on Double-Patterning Lithography," J. Micro/Nanolith. MEMS MOEMS 8(1), 011,001 (2009).

2008

S. H. Chan, A. K. Wong, and E. Y. Lam, "Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography," Opt. Express 16, 14,746-14,760 (2008).

2007

A. Poonawala and P. Milanfar, "Mask design for optical microlithography—an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[PubMed]

2002

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

2000

1997

J. F. Chen, T. Laidig, K. Wampler, and R. Caldwell, "Optical proximity correction for intermediate-pitch features using sub-resolution scattering bars," J. Vac. Sci. Technol. B 15(6), 2426-2433 (1997).

Q4. Y. C. Pati, A. A. Ghazanfarian, and R. F. Pease, "Exploiting Structure in Fast Aerial Image Computation for Integrated Circuit Patterns," IEEE Trans. Semi. Manufactur. 10(1), 62-74 (1997).

1991

Q3. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, "Massively parallel algorithms for scattering in optical lithography," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 10(9), 1091-1100 (1991).

1988

S. Osher and J. A. Sethian, "Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations," J. Comput. Phys. 79, 12-49 (1988).

Q1. D. Nyyssonen and C. P. Kirk, "Optical microscope imaging of lines patterned in thick layers with variable edge geometry: theory," J. Opt. Soc. Am. A 5(8), 1270-1280 (1988).

1987

Q2. T. Matsuzawa, A. Moniwa, N. Hasegawa, and H. Sunami, "Two-Dimensional Simulation of Photolithography on Reflective Stepped Substrate," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 6(3), 446-451 (1987).

1975

F. H. Dill, W. Hornberger, P. Hauge, and J. Shaw, "Characterization of positive photoresists," IEEE Trans. Electron Devices ED-22(7), 445-452 (1975).

K. L. Konnerth and F. H. Dill, "In-situ measurement of dielectric thickness during etching or developing process," IEEE Trans. Electron Devices ED-22(7), 452-456 (1975).

1966

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).

Bukofsky, S.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Caldwell, R.

J. F. Chen, T. Laidig, K. Wampler, and R. Caldwell, "Optical proximity correction for intermediate-pitch features using sub-resolution scattering bars," J. Vac. Sci. Technol. B 15(6), 2426-2433 (1997).

Chan, S. H.

S. H. Chan, A. K. Wong, and E. Y. Lam, "Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography," Opt. Express 16, 14,746-14,760 (2008).

Chen, J. F.

J. F. Chen, T. Laidig, K. Wampler, and R. Caldwell, "Optical proximity correction for intermediate-pitch features using sub-resolution scattering bars," J. Vac. Sci. Technol. B 15(6), 2426-2433 (1997).

Dill, F. H.

F. H. Dill, W. Hornberger, P. Hauge, and J. Shaw, "Characterization of positive photoresists," IEEE Trans. Electron Devices ED-22(7), 445-452 (1975).

K. L. Konnerth and F. H. Dill, "In-situ measurement of dielectric thickness during etching or developing process," IEEE Trans. Electron Devices ED-22(7), 452-456 (1975).

Fonseca, C.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Gamelin, J.

Q3. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, "Massively parallel algorithms for scattering in optical lithography," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 10(9), 1091-1100 (1991).

Ghazanfarian, A. A.

Q4. Y. C. Pati, A. A. Ghazanfarian, and R. F. Pease, "Exploiting Structure in Fast Aerial Image Computation for Integrated Circuit Patterns," IEEE Trans. Semi. Manufactur. 10(1), 62-74 (1997).

Goodman, J. W.

Guerrieri, R.

Q3. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, "Massively parallel algorithms for scattering in optical lithography," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 10(9), 1091-1100 (1991).

Hasegawa, N.

Q2. T. Matsuzawa, A. Moniwa, N. Hasegawa, and H. Sunami, "Two-Dimensional Simulation of Photolithography on Reflective Stepped Substrate," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 6(3), 446-451 (1987).

Hauge, P.

F. H. Dill, W. Hornberger, P. Hauge, and J. Shaw, "Characterization of positive photoresists," IEEE Trans. Electron Devices ED-22(7), 445-452 (1975).

Hibbs, M.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Hornberger, W.

F. H. Dill, W. Hornberger, P. Hauge, and J. Shaw, "Characterization of positive photoresists," IEEE Trans. Electron Devices ED-22(7), 445-452 (1975).

Kirk, C. P.

Konnerth, K. L.

K. L. Konnerth and F. H. Dill, "In-situ measurement of dielectric thickness during etching or developing process," IEEE Trans. Electron Devices ED-22(7), 452-456 (1975).

Lai, K.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Laidig, T.

J. F. Chen, T. Laidig, K. Wampler, and R. Caldwell, "Optical proximity correction for intermediate-pitch features using sub-resolution scattering bars," J. Vac. Sci. Technol. B 15(6), 2426-2433 (1997).

Lam, E. Y.

S. H. Chan, A. K. Wong, and E. Y. Lam, "Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography," Opt. Express 16, 14,746-14,760 (2008).

Q5. E. Y. Lam and J. W. Goodman, "Iterative Statistical Approach to Blind Image Deconvolution," J. Opt. Soc. Am. A 17(7), 1177-1184 (2000).

Matsuzawa, T.

Q2. T. Matsuzawa, A. Moniwa, N. Hasegawa, and H. Sunami, "Two-Dimensional Simulation of Photolithography on Reflective Stepped Substrate," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 6(3), 446-451 (1987).

Milanfar, P.

A. Poonawala and P. Milanfar, "Mask design for optical microlithography—an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[PubMed]

Molless, A. F.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Moniwa, A.

Q2. T. Matsuzawa, A. Moniwa, N. Hasegawa, and H. Sunami, "Two-Dimensional Simulation of Photolithography on Reflective Stepped Substrate," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 6(3), 446-451 (1987).

Neureuther, A.

Q3. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, "Massively parallel algorithms for scattering in optical lithography," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 10(9), 1091-1100 (1991).

Nyyssonen, D.

Osher, S.

S. Osher and J. A. Sethian, "Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations," J. Comput. Phys. 79, 12-49 (1988).

Pati, Y. C.

Q4. Y. C. Pati, A. A. Ghazanfarian, and R. F. Pease, "Exploiting Structure in Fast Aerial Image Computation for Integrated Circuit Patterns," IEEE Trans. Semi. Manufactur. 10(1), 62-74 (1997).

Pease, R. F.

Q4. Y. C. Pati, A. A. Ghazanfarian, and R. F. Pease, "Exploiting Structure in Fast Aerial Image Computation for Integrated Circuit Patterns," IEEE Trans. Semi. Manufactur. 10(1), 62-74 (1997).

Poonawala, A.

A. Poonawala and P. Milanfar, "Mask design for optical microlithography—an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[PubMed]

Rosenbluth, A. E.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Sethian, J. A.

S. Osher and J. A. Sethian, "Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations," J. Comput. Phys. 79, 12-49 (1988).

Shaw, J.

F. H. Dill, W. Hornberger, P. Hauge, and J. Shaw, "Characterization of positive photoresists," IEEE Trans. Electron Devices ED-22(7), 445-452 (1975).

Singh, R. N.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Sunami, H.

Q2. T. Matsuzawa, A. Moniwa, N. Hasegawa, and H. Sunami, "Two-Dimensional Simulation of Photolithography on Reflective Stepped Substrate," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 6(3), 446-451 (1987).

Tadros, K. H.

Q3. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, "Massively parallel algorithms for scattering in optical lithography," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 10(9), 1091-1100 (1991).

Wampler, K.

J. F. Chen, T. Laidig, K. Wampler, and R. Caldwell, "Optical proximity correction for intermediate-pitch features using sub-resolution scattering bars," J. Vac. Sci. Technol. B 15(6), 2426-2433 (1997).

Wong, A. K.

S. H. Chan, A. K. Wong, and E. Y. Lam, "Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography," Opt. Express 16, 14,746-14,760 (2008).

Wong, A. K. K.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).

Aided Des. Int. Cir. Sys.

Q2. T. Matsuzawa, A. Moniwa, N. Hasegawa, and H. Sunami, "Two-Dimensional Simulation of Photolithography on Reflective Stepped Substrate," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 6(3), 446-451 (1987).

Q3. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, "Massively parallel algorithms for scattering in optical lithography," IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 10(9), 1091-1100 (1991).

IEEE Trans. Antennas Propag.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).

IEEE Trans. Electron Devices

F. H. Dill, W. Hornberger, P. Hauge, and J. Shaw, "Characterization of positive photoresists," IEEE Trans. Electron Devices ED-22(7), 445-452 (1975).

K. L. Konnerth and F. H. Dill, "In-situ measurement of dielectric thickness during etching or developing process," IEEE Trans. Electron Devices ED-22(7), 452-456 (1975).

IEEE Trans. Image Process.

A. Poonawala and P. Milanfar, "Mask design for optical microlithography—an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[PubMed]

IEEE Trans. Semi. Manufactur.

Q4. Y. C. Pati, A. A. Ghazanfarian, and R. F. Pease, "Exploiting Structure in Fast Aerial Image Computation for Integrated Circuit Patterns," IEEE Trans. Semi. Manufactur. 10(1), 62-74 (1997).

J. Comput. Phys.

S. Osher and J. A. Sethian, "Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations," J. Comput. Phys. 79, 12-49 (1988).

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

J. F. Chen, T. Laidig, K. Wampler, and R. Caldwell, "Optical proximity correction for intermediate-pitch features using sub-resolution scattering bars," J. Vac. Sci. Technol. B 15(6), 2426-2433 (1997).

Microsyst.

Q6. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., Microsyst. 1(1), 13-30 (2002).

Opt. Express

S. H. Chan, A. K. Wong, and E. Y. Lam, "Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography," Opt. Express 16, 14,746-14,760 (2008).

Other

J. A. Sethian, "Fast marching level set methods for three-dimensional photolithography development," in Proc. SPIE, G. Fuller, ed., vol. 2726, pp. 262-272 (1996).

B. Yenikaya and A. Sezginer, "A rigorous method to determine printability of a target layout," in Proc. SPIE, A. K. K. Wong and V. K. Singh, eds., vol. 6521, p. 652112 (2007).

N. Jia, A. K. Wong, and E. Y. Lam, "Robust Photomask Design with Defocus Variation Using Inverse Synthesis," in Proc. SPIE, vol. 7140, p. 71401W (2008).

A. E. Rosenbluth, G. Gallatin, R. Gordon, W. Hinsberg, J. Hoffnagle, F. Houle, K. Lai, A. Lvov, M. Sanchez, and N. Seong, "Fast calculation of images for high numerical aperture lithography," in Proc. SPIE, B. Smith, ed., vol. 5377, pp. 615-628 (2004).

M. Born and E. Wolf, Principles of Optics, pp. 491-555, sixth ed. (Pergamon Press, 1980).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2001).

A. K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005).

J. Kim and M. Fan, "Hotspot detection on post-OPC layout using full-chip simulation-based verification tool: a case study with aerial image simulation," in Proc. SPIE, K. R. Kimmel and W. Staud, eds., vol. 5256, pp. 919-925 (2003).

S. D. Shang, Y. Granik, N. B. Cobb, W. Maurer, Y. Cui, L. W. Liebmann, J. M. Oberschmidt, R. N. Singh, and B. R. Vampatella, "Failure prediction across process window for robust OPC," in Proc. SPIE, A. Yen, ed., vol. 5040, pp. 431-440 (2003).

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Figures (4)

Fig. 1.
Fig. 1.

Illustration of a projection microlithography exposure system [26].

Fig. 2.
Fig. 2.

An example of inverse lithography with no regularization.

Fig. 3.
Fig. 3.

An example of inverse lithography designed for robustness against defocus.

Fig. 4.
Fig. 4.

The reality-virtuality space of computation lithography (not to scale).

Equations (10)

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I xy = + w (xxo,yyo;xxo,yyo) O (xo,yo) O* (xo,yo) d xo d yo d xo d yo ,
where w (xo,yo;xo,yo) =J (xoxo,yoyo) H (xo,yo)H*(xo,yo),
J (xoxo,yoyo) is the mutual intensity ,
H xy is the optical system transfer function ,
O xy is the mask transmittance ,
I ( x , y ) k=1Kλk ∫∫−∞+∞φk(xx,yy) O ( x , y ) dx d y 2 .
I xy k=1K n=1Ntfg [ψk(xx1(n),yy1(n))ψk(xx2(n),yy1(n))+
ψk(xx2(n),yy2(n))ψk(xx1(n),yy2(n))] 2 ,
Oopt xy =argOxymin{0,1} Σx,y[11+exp{a(HxyOxy2tr)}Îxy]2
Oopt xy =argOxymin{0,1} β{Σx,y[11+exp{a(HxyOxy2tr)}Îxy]2},

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