Joint trajectories of brain atrophy, white matter hyperintensities and cognition quantify brain maintenance.
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- [1] § Results › Longitudinal interrelations across neurocognitive domains of ageing-related atrophy, WMH, and cognition ↔ R/lgcm_syntax.R, lines 159–279 · score 0.51 · residual coupling, trivariate LGCM, cross, M48, variances, manifest
Paper
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The authors' code
R · 279 lines · 11 KB · GPL-3.0 · 1 match
- # brain-maintenance-lgcm: trivariate latent growth curve model and brain
- # maintenance index, companion code for Menze et al. (2026).
- #
- # Copyright (C) 2026 The authors of Menze et al. (2026).
- #
- # This program is free software: you can redistribute it and/or modify it
- # under the terms of the GNU General Public License as published by the
- # Free Software Foundation, either version 3 of the License, or (at your
- # option) any later version.
- #
- # This program is distributed in the hope that it will be useful, but
- # WITHOUT ANY WARRANTY; without even the implied warranty of
- # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- # General Public License for more details: <https://www.gnu.org/licenses/>.
- # =============================================================================
- # lgcm_syntax.R
- # -----------------------------------------------------------------------------
- # Builders for the lavaan model syntax of the trivariate latent growth curve
- # model (LGCM) described in:
- # Menze, Ziegler, ..., Düzel (2025/26). Joint trajectories of brain atrophy,
- # white matter hyperintensities and cognition quantify brain maintenance.
- #
- # Two construction helpers (`measurement_block` and `measurement_block_quad`)
- # emit the measurement / loading equations for one construct, with either a
- # linear or a linear-plus-quadratic latent slope. A third helper
- # (`cross_residuals`) emits time-matched residual covariances between
- # constructs ("cross-construct couplings").
- #
- # The top-level entry point `build_trivariate_lgcm()` assembles the full model
- # string from these blocks plus the structural equations for covariate
- # regressions and latent factor covariances.
- #
- # Design choice: all model text is generated programmatically rather than
- # hard-coded, so that changing the set of time points (e.g. T = 4 vs T = 5)
- # does not require manual edits. The slope identifiability constraints are
- # documented in docs/model_specification.md.
- # =============================================================================
- #' Build the measurement / loading block for one linear-slope construct.
- #'
- #' @param prefix Variable prefix common to all time points (e.g. "cog_z_").
- #' @param time_points Character vector of time-point suffixes (e.g. "M00").
- #' @param intercept_name Name of the latent intercept factor.
- #' @param slope_name Name of the latent linear-slope factor.
- #' @param residual_label A label used to constrain residual variances to be
- #' equal across time (homoscedastic residuals). Use distinct labels per
- #' construct (e.g. "a", "b", "c") to keep parameters separated.
- #' @param free_manifest_intercepts Logical. If FALSE (default), all manifest
- #' intercepts are fixed to 0 so that the latent intercept absorbs the mean.
- #' If TRUE, the first time point is fixed to 0 and the remaining time
- #' points share a free intercept "pr" — this corresponds to the
- #' practice-effect parameterisation used for cognition in the original
- #' manuscript.
- #' @return A character string of lavaan syntax.
- measurement_block <- function(prefix,
- time_points,
- intercept_name,
- slope_name,
- residual_label = "x",
- free_manifest_intercepts = FALSE) {
- intercept_lines <- paste0(
- intercept_name, " =~ ",
- paste0("1*", prefix, time_points, collapse = " + ")
- )
- slope_lines <- paste0(
- slope_name, " =~ ",
- paste0(seq_along(time_points) - 1L, "*", prefix, time_points,
- collapse = " + ")
- )
- residuals <- paste0(
- prefix, time_points, " ~~ ", residual_label, "*", prefix, time_points,
- collapse = "\n"
- )
- if (isTRUE(free_manifest_intercepts)) {
- intcpts <- paste0(
- prefix, time_points,
- ifelse(time_points == time_points[1L], " ~ 0", " ~ pr*1"),
- collapse = "\n"
- )
- } else {
- intcpts <- paste0(prefix, time_points, " ~ 0", collapse = "\n")
- }
- paste(intercept_lines, slope_lines, residuals, intcpts, sep = "\n")
- }
- #' Build the measurement / loading block for a construct with both linear
- #' and quadratic latent slopes.
- #'
- #' Loadings for the quadratic slope are fixed to (t - 1)^2 for the t-th time
- #' point, i.e. {0, 1, 4, 9, 16} for the five-occasion design.
- #'
- #' @inheritParams measurement_block
- #' @param slope_q_name Name of the latent quadratic-slope factor.
- #' @return A character string of lavaan syntax.
- measurement_block_quad <- function(prefix,
- time_points,
- intercept_name,
- slope_name,
- slope_q_name,
- residual_label = "x") {
- intercept_lines <- paste0(
- intercept_name, " =~ ",
- paste0("1*", prefix, time_points, collapse = " + ")
- )
- slope_lines <- paste0(
- slope_name, " =~ ",
- paste0(seq_along(time_points) - 1L, "*", prefix, time_points,
- collapse = " + ")
- )
- slopeq_lines <- paste0(
- slope_q_name, " =~ ",
- paste0((seq_along(time_points) - 1L)^2, "*", prefix, time_points,
- collapse = " + ")
- )
- residuals <- paste0(
- prefix, time_points, " ~~ ", residual_label, "*", prefix, time_points,
- collapse = "\n"
- )
- intcpts <- paste0(prefix, time_points, " ~ 0", collapse = "\n")
- paste(intercept_lines, slope_lines, slopeq_lines, residuals, intcpts,
- sep = "\n")
- }
- #' Build time-matched cross-construct residual covariances.
- #'
- #' For each occasion t, this adds a covariance between the residuals of
- #' prefix1_t and prefix2_t, constrained to be equal across time using the
- #' supplied label (e.g. "x*").
- #'
- #' @param prefix1,prefix2 Variable prefixes of the two constructs.
- #' @param time_points Time-point suffixes.
- #' @param residual_label Lavaan label, including the "*" multiplier
- #' (default "x*"). Use distinct labels per construct pair.
- #' @return A character string of lavaan syntax.
- cross_residuals <- function(prefix1, prefix2, time_points,
- residual_label = "x*") {
- paste0(
- prefix1, time_points, " ~~ ", residual_label, prefix2, time_points,
- collapse = "\n"
- )
- }
- #' Assemble the full trivariate LGCM syntax used in the manuscript.
- #'
- #' Defaults match the published model:
- #' - linear slope for cognition and WMH
- #' - linear + quadratic slope for the atrophy proxy
- #' - free practice-effect intercept ("pr") for cognition (manifest
- #' intercepts at all post-baseline occasions)
- #' - covariates: age_z, sex_z, edyrs_z, tiv_z (standardised)
- #' - homoscedastic residuals per construct (labels a / b / c)
- #' - time-matched cross-construct residual couplings (labels x* / y* / z*)
- #'
- #' The covariate model treats age, sex, education, and TIV as exogenous
- #' standardised variables (means fixed to 0, variances fixed to 1) and
- #' freely estimates pairwise covariances among them. APOE-epsilon4 and
- #' vascular-risk covariates are commented in the syntax for transparency
- #' and can be enabled by extending the formula.
- #'
- #' @param time_points Character vector of T time-point suffixes (T >= 3 for
- #' identifiability of a linear slope, T >= 4 for a quadratic slope).
- #' @param prefix_cog,prefix_wmh,prefix_brain Variable prefixes.
- #' @return A length-one character string containing the lavaan model.
- build_trivariate_lgcm <- function(time_points = c("M00", "M12", "M24",
- "M36", "M48"),
- prefix_cog = "cog_z_",
- prefix_wmh = "wmh_z_",
- prefix_brain = "atrophy_z_") {
- stopifnot(length(time_points) >= 4L) # quadratic slope needs T >= 4
- cog_block <- measurement_block(prefix_cog, time_points,
- "intcept_cog", "slope_linear_cog",
- residual_label = "a",
- free_manifest_intercepts = TRUE)
- wmh_block <- measurement_block(prefix_wmh, time_points,
- "intcept_wmh", "slope_linear_wmh",
- residual_label = "b",
- free_manifest_intercepts = FALSE)
- brain_block <- measurement_block_quad(prefix_brain, time_points,
- "intcept_brain", "slope_linear_brain",
- "slope_q",
- residual_label = "c")
- cog_wmh <- cross_residuals(prefix_cog, prefix_wmh, time_points, "x*")
- cog_brain <- cross_residuals(prefix_cog, prefix_brain, time_points, "y*")
- wmh_brain <- cross_residuals(prefix_wmh, prefix_brain, time_points, "z*")
- glue::glue('
- # === COG ====================================================================
- {cog_block}
- intcept_cog ~ 1 + age_z + sex_z + edyrs_z
- slope_linear_cog ~ 1 + age_z + sex_z + edyrs_z
- intcept_cog ~~ slope_linear_cog
- intcept_cog ~~ intcept_cog
- slope_linear_cog ~~ slope_linear_cog
- # === WMH ====================================================================
- {wmh_block}
- intcept_wmh ~ 1 + age_z + sex_z + edyrs_z + tiv_z
- slope_linear_wmh ~ 1 + age_z + sex_z + edyrs_z + tiv_z
- intcept_wmh ~~ slope_linear_wmh
- intcept_wmh ~~ intcept_wmh
- slope_linear_wmh ~~ slope_linear_wmh
- # === BRAIN (linear + quadratic) =============================================
- {brain_block}
- intcept_brain ~ 1 + age_z + sex_z + edyrs_z + tiv_z
- slope_linear_brain ~ 1 + age_z + sex_z + edyrs_z + tiv_z
- slope_q ~ 1 + age_z + sex_z + edyrs_z + tiv_z
- intcept_brain ~~ slope_linear_brain + slope_q
- intcept_brain ~~ intcept_brain
- slope_linear_brain ~~ slope_linear_brain
- slope_q ~~ slope_q
- slope_linear_brain ~~ slope_q
- # === Domain couplings (latent factor covariances) ===========================
- intcept_wmh ~~ intcept_cog
- intcept_wmh ~~ slope_linear_cog
- intcept_cog ~~ slope_linear_wmh
- slope_linear_wmh ~~ slope_linear_cog
- intcept_wmh ~~ intcept_brain
- intcept_wmh ~~ slope_linear_brain
- intcept_brain ~~ slope_linear_wmh
- slope_linear_wmh ~~ slope_linear_brain
- intcept_brain ~~ intcept_cog
- intcept_brain ~~ slope_linear_cog
- intcept_cog ~~ slope_linear_brain
- slope_linear_brain ~~ slope_linear_cog
- slope_q ~~ intcept_cog + intcept_wmh + slope_linear_cog + slope_linear_wmh
- # === Covariate (exogenous) model ============================================
- age_z ~ 0*1
- sex_z ~ 0*1
- tiv_z ~ 0*1
- edyrs_z ~ 0*1
- age_z ~~ 1*age_z
- sex_z ~~ 1*sex_z
- tiv_z ~~ 1*tiv_z
- edyrs_z ~~ 1*edyrs_z
- age_z ~~ sex_z + tiv_z + edyrs_z
- sex_z ~~ tiv_z + edyrs_z
- tiv_z ~~ edyrs_z
- # === Cross-construct residual couplings (time-matched) ======================
- {cog_wmh}
- {cog_brain}
- {wmh_brain}
- ')
- }
lgcm_syntax.R at commit 8dac647, under GPL-3.0 · at the source
Overview
and 29 other authors
Daniel Janowitz11,12, Ingo Kiliman20,21, Luca Kleineidam14,15, Marie Theres Kronmüller14, Christoph Laske22,23, Debora Melo van Lent24, Falk Lüsebrink1, Robert Perneczky11,25,26,27, Oliver Peters8,16,17, Lukas Preis16, Josef Priller4,8,9,28, Boris-Stephan Rauchmann25,29,30, Ayda Rostamzadeh31, Sandra Roeske14, Klaus Scheffler32, Björn-Hendrik Schott10,33,34, Anja Schneider14,15, Sebastian Sodenkamp22,35, Annika Spottke14,36, Eike Jakob Spruth8,9, Melina Stark14,15, Stefan Teipel20,21, Michael Wagner14,15, Jens Wiltfang10,33,37, Frank Jessen14,31,38, Alfredo Ramirez7,14,15,24,38, Stefanie Schreiber1,39, Emrah Düzel1,2,40, Gabriel Ziegler1,240 affiliations
- German Centre for Neurodegenerative Diseases (DZNE),Magdeburg, Germany
- Institute of Cognitive Neurology and Dementia Research, Otto von Guericke University Magdeburg,Magdeburg, Germany
- Department Artificial Intelligence in Biomedical Engineering (AIBE), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU),Erlangen, Germany
- Institute for Neuroscience and Cardiovascular Research, Row Fogo Centre for Research into Ageing and The Brain, Department of Neuroimaging Sciences, The University of Edinburgh,Edinburgh, UK
- Faculty of Medicine, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU),Erlangen, Germany
- Donders Institute for Brain, Cognition and Behavior, Radboud University Medical Centre,Nijmegen, The Netherlands
- Division of Neurogenetics and Molecular Psychiatry, Department of Psychiatry and Psychotherapy, Faculty of Medicine and University Hospital Cologne, University of Cologne,Cologne, Germany
- German Centre for Neurodegenerative Diseases (DZNE),Berlin, Germany
- Department of Psychiatry and Psychotherapy, Charité,Berlin, Germany
- Department of Psychiatry and Psychotherapy, University Medical Centre Goettingen, Georg August University of Goettingen,Goettingen, Germany
- German Centre for Neurodegenerative Diseases (DZNE),Munich, Germany
- Institute for Stroke and Dementia Research (ISD), University Hospital, LMU Munich,Munich, Germany
- MR-Research in Neurosciences, Department of Cognitive Neurology, University Medical Centre Goettingen,Goettingen, Germany
- German Centre for Neurodegenerative Diseases (DZNE),Bonn, Germany
- Department of Old Age Psychiatry and Cognitive Disorders, University of Bonn, University Hospital Bonn,Bonn, Germany
- Department of Psychiatry and Neurosciences, Charité Universitätsmedizin Berlin,Berlin, Germany
- Charité Universitätsmedizin Berlin, ECRC Experimental and Clinical Research Center,Berlin, Germany
- Berlin Centre for Advanced Neuroimaging, Charité – Universitätsmedizin Berlin,Berlin, Germany
- Vivantes Klinikum Am Urban, Department of Psychiatry, Psychotherapy, and Psychosomatics, Vivantes Urban Hospital,Berlin, Germany
- German Centre for Neurodegenerative Diseases (DZNE),Rostock, Germany
- Department of Psychosomatic Medicine, Rostock University Medical Center,Rostock, Germany
- German Centre for Neurodegenerative Diseases (DZNE),Tübingen, Germany
- Section for Dementia Research, Hertie Institute for Clinical Brain Research and Department of Psychiatry and Psychotherapy, University of Tübingen,Tübingen, Germany
- Glenn Biggs Institute for Alzheimer’s and Neurodegenerative Diseases, UT Health San Antonio,San Antonio, TX USA
- Department of Psychiatry and Psychotherapy, University Hospital, LMU Munich,Munich, Germany
- Munich Cluster for Systems Neurology (SyNergy),Munich, Germany
- Ageing Epidemiology Research Unit (AGE), School of Public Health, Imperial College London, Charing Cross Hospital,London, UK
- Department of Psychiatry and Psychotherapy, School of Medicine and Health, Technical University of Munich, and German Centre for Mental Health (DZPG),Munich, Germany
- Sheffield Institute for Translational Neuroscience (SITraN), University of Sheffield,Sheffield, UK
- Department of Neuroradiology, University Hospital LMU,Munich, Germany
- Department of Psychiatry, University of Cologne, Medical Faculty,Cologne, Germany
- Department for Biomedical Magnetic Resonance, University of Tübingen,Tübingen, Germany
- German Centre for Neurodegenerative Diseases (DZNE),Goettingen, Germany
- Leibniz Institute for Neurobiology,Magdeburg, Germany
- Department of Psychiatry and Psychotherapy, University of Tübingen,Tübingen, Germany
- Department of Neurology, University of Bonn,Bonn, Germany
- Neurosciences and Signaling Group, Institute of Biomedicine (iBiMED), Department of Medical Sciences, University of Aveiro, Campus Universitario de Santiago,Aveiro, Portugal
- Excellence Cluster on Cellular Stress Responses in Aging-Associated Diseases (CECAD), University of Cologne,Cologne, Germany
- Department of Neurology, Otto von Guericke University Magdeburg,Magdeburg, Germany
- Institute of Cognitive Neuroscience, University College London,London, UK
Abstract
Brain maintenance – the preservation of brain structure or function relevant to cognitive performance – remains challenging to quantify. Here, we propose a domain-general brain maintenance index derived by jointly modelling the longitudinal co-evolution of ageing-related atrophy (via medial temporal lobe to ventricle ratio, MTLV-ratio), white matter hyperintensities (WMH), and global cognition assessed by the preclinical Alzheimer’s cognitive composite (PACC5) using latent growth curve modelling. We demonstrate its utility in 543 cognitively unimpaired older adults from the DELCODE cohort, followed annually over four years. We show that changes in MTLV-ratio and WMH additively predict cognitive change. We further show that higher neuroticism, depressive symptoms, lower openness, and faster biological ageing are related to unfavourable domain-specific trajectories and poorer brain maintenance. Our findings highlight the combined relevance of WMH and ageing-related atrophy dynamics for brain maintenance. Maintaining cerebrovascular and mental health alongside cognitive engagement could promote brain maintenance, delay cognitive decline and dementia.
Reproduced under the paper's license (CC BY), from the paper cited above.
Repository
Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.
neuroprognosis/brain-maintenance-lgcm
8dac647ebc7e88a098f6a70d89cd47e1de0671ef, 22 May 2026Availability: 1 check, the latest on 27 September 2026: the link answers
- 27 September 2026: the link answers
13 files
- R/
fit_model.R , R, 107 lines - R/
lgcm_syntax.R , R, 279 lines, 1 match - R/
maintenance_index.R , R, 125 lines - R/
preprocess.R , R, 99 lines - R/
simulate_data.R , R, 207 lines - data-raw/
make_synthetic_data.R , R, 50 lines - scripts/
run_analysis.R , R, 117 lines - tests/
testthat.R , R, 49 lines - tests/
testthat/ , R, 90 linestest-pipeline.R - tests/
testthat/ , R, 58 linestest-preprocess.R - tests/
testthat/ , R, 82 linestest-syntax.R - LICENSE, License, 674 lines
- README.md, Text, 202 lines
Code availability
The R code implementing the trivariate latent growth curve model (lavaan syntax), factor-score extraction, and robust regression for the brain maintenance index is openly available at https://
Reproduced under the paper's license (CC BY), from the paper cited above.
Tracing map
Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.
What the map holds:
- 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
- 11 scripts, each with its path and the digest of its content;
- 1 match between paragraphs of the paper and lines of the code (method lexical-v1);
- neither the text of the paper nor the code itself.
Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.
Data
No dataset and no data link were found in the paper.
Data availability
The raw data collected in the study DELCODE—DZNE-Longitudina
Reproduced under the paper's license (CC BY), from the paper cited above.
Versions
The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.
Version 1, 27 September 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 49 authors, 4 keywords, 12 MeSH terms, 95 references.
Cite
This paper
Menze, I., Bernal, J., Kievit, R. A., Tripathi, K. P., Kaleck, T., Yakupov, R., Altenstein, S., Bartels, C., Buerger, K., Butryn, M., Dechent, P., Ewers, M., Fliessbach, K., Frommann, I., Gemenetzi, M., Glanz, W., Gref, D., Hellmann-Regen, J., Hetzer, S., . . . Ziegler, G. (2026). Joint trajectories of brain atrophy, white matter hyperintensities and cognition quantify brain maintenance. Nature communications, 17(1), 5846. https://
BibTeX
@article{menze2026joint,
author = {Menze, Inga and Bernal, Jose and Kievit, Rogier A. and Tripathi, Kumar Parijat and Kaleck, Timo and Yakupov, Renat and Altenstein, Slawek and Bartels, Claudia and Buerger, Katharina and Butryn, Michaela and Dechent, Peter and Ewers, Michael and Fliessbach, Klaus and Frommann, Ingo and Gemenetzi, Maria and Glanz, Wenzel and Gref, Daria and Hellmann-Regen, Julian and Hetzer, Stefan and Incesoy, Enise I. and Janowitz, Daniel and Kiliman, Ingo and Kleineidam, Luca and Kronmüller, Marie Theres and Laske, Christoph and van Lent, Debora Melo and Lüsebrink, Falk and Perneczky, Robert and Peters, Oliver and Preis, Lukas and Priller, Josef and Rauchmann, Boris-Stephan and Rostamzadeh, Ayda and Roeske, Sandra and Scheffler, Klaus and Schott, Björn-Hendrik and Schneider, Anja and Sodenkamp, Sebastian and Spottke, Annika and Spruth, Eike Jakob and Stark, Melina and Teipel, Stefan and Wagner, Michael and Wiltfang, Jens and Jessen, Frank and Ramirez, Alfredo and Schreiber, Stefanie and Düzel, Emrah and Ziegler, Gabriel},
title = {{Joint trajectories of brain atrophy, white matter hyperintensities and cognition quantify brain maintenance}},
journal = {Nature communications},
year = {2026},
month = jul,
volume = {17},
number = {1},
pages = {5846},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/
url = {https://
pmid = {42401584},
pmcid = {PMC13332871}
}
RIS
TY - JOUR
AU - Menze, Inga
AU - Bernal, Jose
AU - Kievit, Rogier A.
AU - Tripathi, Kumar Parijat
AU - Kaleck, Timo
AU - Yakupov, Renat
AU - Altenstein, Slawek
AU - Bartels, Claudia
AU - Buerger, Katharina
AU - Butryn, Michaela
AU - Dechent, Peter
AU - Ewers, Michael
AU - Fliessbach, Klaus
AU - Frommann, Ingo
AU - Gemenetzi, Maria
AU - Glanz, Wenzel
AU - Gref, Daria
AU - Hellmann-Regen, Julian
AU - Hetzer, Stefan
AU - Incesoy, Enise I.
AU - Janowitz, Daniel
AU - Kiliman, Ingo
AU - Kleineidam, Luca
AU - Kronmüller, Marie Theres
AU - Laske, Christoph
AU - van Lent, Debora Melo
AU - Lüsebrink, Falk
AU - Perneczky, Robert
AU - Peters, Oliver
AU - Preis, Lukas
AU - Priller, Josef
AU - Rauchmann, Boris-Stephan
AU - Rostamzadeh, Ayda
AU - Roeske, Sandra
AU - Scheffler, Klaus
AU - Schott, Björn-Hendrik
AU - Schneider, Anja
AU - Sodenkamp, Sebastian
AU - Spottke, Annika
AU - Spruth, Eike Jakob
AU - Stark, Melina
AU - Teipel, Stefan
AU - Wagner, Michael
AU - Wiltfang, Jens
AU - Jessen, Frank
AU - Ramirez, Alfredo
AU - Schreiber, Stefanie
AU - Düzel, Emrah
AU - Ziegler, Gabriel
TI - Joint trajectories of brain atrophy, white matter hyperintensities and cognition quantify brain maintenance
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/
VL - 17
IS - 1
SP - 5846
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/
UR - https://
LA - en
ER -
CSL-JSON
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"page": "5846",
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[
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7,
4
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]
}
}
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