25:["$","title",null,{"children":"Task 1 for Multidimensional Data | Friederike's Workspace | Observable"}] 49:T686,chartClustered = { const svg = d3.select(DOM.svg(width, height)); svg.node().drawData = function (threshold) { svg.selectAll('g').remove() const g = svg .attr('width', width - margin.left) .attr('height', height + margin.top + margin.bottom) .append('g') .attr('transform', 'translate(' + margin.left + ', 0)'); g.append('g') .attr('transform', 'translate(0,' + height + ')') .call(d3.axisBottom(x_scale)) .selectAll("text") .style("text-anchor", "end") .attr("dx", "-.8em") .attr("dy", ".15em") .attr("transform", "rotate(-65)"); let dataPerGene = separateByGene(data) let clusteredData = upgma(dataPerGene, threshold) let heightCell = height / (dataPerGene.length + 2 * (clusteredData.length - 1)) let currentHeight = height for (let i = 0; i < clusteredData.length; i++) { let numberChildren = clusteredData[i].flat_children.length let newYScale = d3.scaleBand() .domain(clusteredData[i].flat_children) .range([currentHeight,currentHeight - (numberChildren * heightCell)]) g.append('g').call(d3.axisLeft(newYScale)); let currentCluster = data.filter((key) => clusteredData[i].flat_children.includes(key.y)) svg .selectAll() .data(currentCluster) .enter() .append('rect') .attr('x', d => x_scale(d.x) + margin.left) .attr('y', d => newYScale(d.y)) .attr('width', x_scale.bandwidth() ) .attr('height', heightCell) .attr('fill', d => color_scale(d.value)); currentHeight = currentHeight - (numberChildren * heightCell) - (2 * heightCell) } } return svg.node(); } 4a:T585,function helper_upgma(distanceMatrix, threshold, input_cluster) { // Where in this function could we use the threshold variable to create disjoint clusters? let distMat = structuredClone(distanceMatrix) let clusters = structuredClone(input_cluster) while (clusters.length > 1) { // Find the minimum distance and corresponding clusters const { minDistance, clusterIndices } = findMinDistance(distMat); if (minDistance > threshold) { break } let arrayChildrenCluster1 = clusters[clusterIndices[0]].flat_children let arrayChildrenCluster2 = clusters[clusterIndices[1]].flat_children // Merge the two closest clusters into a new cluster const newCluster = new Cluster( 'Cluster' + clusters.length, clusters[clusterIndices[0]].size + clusters[clusterIndices[1]].size, arrayChildrenCluster1.concat(arrayChildrenCluster2) ); newCluster.addChild(clusters[clusterIndices[0]], minDistance/2); newCluster.addChild(clusters[clusterIndices[1]], minDistance/2); distMat = updateDistanceMatrix(distMat, clusterIndices, clusters) // Remove the merged clusters from the list clusters.splice(clusterIndices[0], 1); clusters.splice(clusterIndices[1] - 1, 1); // Add the new cluster to the list clusters.push(newCluster); } return clusters; }4b:[{"id":"fb3423f91270c648fade5563b88f5711d7f8a882818f4cd8a65386fdb501de2716ca45b1dc3e8d8307b7024d7f53aa7b5231ded73c2cd08ac89a6ab784bce870","href":"https://static.observableusercontent.com/files/fb3423f91270c648fade5563b88f5711d7f8a882818f4cd8a65386fdb501de2716ca45b1dc3e8d8307b7024d7f53aa7b5231ded73c2cd08ac89a6ab784bce870","name":"znormalized_counts@5.txt","type":"text/plain","lastModified":1694091557754.773,"size":24197},{"id":"cca9dc80c8dbf355359ca3658d4b0831f1df8c939443f410c296f5f1d76f21b7a5f85a8c3879b97f213019f1179c397b0e4bce4a5df2a4fa0aac7ee668deb930","href":"https://static.observableusercontent.com/files/cca9dc80c8dbf355359ca3658d4b0831f1df8c939443f410c296f5f1d76f21b7a5f85a8c3879b97f213019f1179c397b0e4bce4a5df2a4fa0aac7ee668deb930","name":"znormalized_counts_subset.txt","type":"text/plain","lastModified":1694091557754.773,"size":1486}] 29:{"id":"e17ddeefff293c95","slug":null,"title":"Task 1 for Multidimensional Data","thumbnail":"e3db3b108d4983605c00f6ae8d2501999290f31bf2c3dc9f7303f24e38264f6b","access_level":"public","create_time":"$D2023-09-07T12:59:17.754Z","update_time":"$D2023-09-07T15:01:28.871Z","view_time":null,"first_public_time":"$D2023-09-29T10:48:40.596Z","has_unpublished_edits":null,"fork":{"id":"92e88ee2f0b0f6cf","slug":null,"title":"Task 1 for Multidimensional Data","owner":{"id":"70b8a8bf6af1277c","login":"biovis-pract","name":"BioVis-Pract"}},"stars":0,"starred":false,"owner":{"type":"team","id":"76369c69faffe9a6","login":"friederike-ws","name":"Friederike's Workspace","avatar_url":"https://avatars-next.observableusercontent.com/29136d3ec66cad4c1c6a1aba1faa1a59343d987b5df9e7c48d705e829dbb47c3","tier":"starter_2024","bio":"","followed_by_you":false,"follows_you":false},"version":710,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"b8f7d568d2fe50fa","login":"friederike","name":"Friederike","avatar_url":"https://avatars-next.observableusercontent.com/caafbe50892f07fc122c722c4416e549681796ff90a65bba4c1f2bf05b967b84","tier":null,"bio":"","followed_by_you":false,"follows_you":false}],"members":[{"type":"individual","id":"b8f7d568d2fe50fa","login":"friederike","name":"Friederike","avatar_url":"https://avatars-next.observableusercontent.com/caafbe50892f07fc122c722c4416e549681796ff90a65bba4c1f2bf05b967b84","tier":null,"role":"editor"},{"type":"team","id":"76369c69faffe9a6","login":"friederike-ws","name":"Friederike's Workspace","avatar_url":"https://avatars-next.observableusercontent.com/29136d3ec66cad4c1c6a1aba1faa1a59343d987b5df9e7c48d705e829dbb47c3","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Task 1 for Multidimensional Data","cells":[{"id":0,"value":"# Task 1 for Multidimensional Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":536,"value":"## A clustered Heat Map with separation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":549,"value":"#### DATA PREPROCESSING","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":540,"value":"For this, we have prepared a data set of 100 genes across 12 samples. The data has been normalized using Z-score normalization per column. ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":103,"value":"input_counts = FileAttachment(\"znormalized_counts@5.txt\").text()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":542,"value":"This is just a smaller set of the above data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":274,"value":"subset_counts = FileAttachment(\"znormalized_counts_subset.txt\").text()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":544,"value":"We parse the data and include it here for further visualization","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":90,"value":"znormalized_counts = d3.csvParse(input_counts)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":546,"value":"From wide data, we require \"long-data\", so we need to create one object per rectangle.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":116,"value":"data = {\n let tempData = []\n for (let datum of znormalized_counts){\n for (let sample of Object.keys(datum)) {\n if (sample === \"Geneid\")\n continue\n tempData.push({y: datum.Geneid, x: sample, value: parseFloat(datum[sample])})\n }\n }\n return tempData\n \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":552,"value":"### Extracting data for visualization","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":128,"value":"samples = Object.keys(znormalized_counts[0]).filter(d => \"Geneid\" !== d)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"x_scale = d3\n .scaleBand()\n .domain(samples)\n .range([0, width - margin.right])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"genes = new Set(znormalized_counts.map(d => d.Geneid))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":113,"value":"y_scale = d3\n .scaleBand()\n .domain(genes)\n .range([height, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":174,"value":"extent = d3.extent(data.map(d=> d.value))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":589,"value":"average = d3.mean(data.map(d=> d.value))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":81,"value":"color_scale = d3.scaleDiverging()\n .domain([extent[0],0, extent[1]]) //.domain([extent[0],(extent[0] + extent[1]) /2, extent[1]])\n .interpolator(d3.interpolateRdBu)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":83,"value":"margin = ({ top: 10, left: 150, right: 40, bottom: 50 })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"height = 1000","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":559,"value":"### A simple Heatmap","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":78,"value":"chart = {\n const svg = d3.select(DOM.svg(width, height));\n const g = svg\n .attr('width', width - margin.left)\n .attr('height', height + margin.top + margin.bottom)\n .append('g')\n .attr('transform', 'translate(' + margin.left + ', 0)');\n\n g.append('g')\n .attr('transform', 'translate(0,' + height + ')')\n .call(d3.axisBottom(x_scale))\n .selectAll(\"text\")\n .style(\"text-anchor\", \"end\")\n .attr(\"dx\", \"-.8em\")\n .attr(\"dy\", \".15em\")\n .attr(\"transform\", \"rotate(-65)\");\n \n g.append('g').call(d3.axisLeft(y_scale));\n\n svg\n .selectAll()\n .data(data)\n .enter()\n .append('rect')\n .attr('x', d => x_scale(d.x) + margin.left)\n .attr('y', d => y_scale(d.y))\n .attr('width', x_scale.bandwidth() )\n .attr('height', y_scale.bandwidth() )\n .attr('fill', d => color_scale(d.value));\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":561,"value":"As you can see here, the heatmap does not really provide much information on the similarity across genes nor samples. We will start just by clustering the genes (aka rows) of the heatmap. \n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":563,"value":"## Tasks: \n- First, by using the helper functions found at the bottom of this notebook, cluster the genes using either the euclidean distance or the spearman distance provided.\n- - Adapt the data so that you get one array per gene\n - Run the simple version of UPGMA that clusters all input without creating any disjoint clusters (UPGMA is a hierarchichal algorithm)\n- We will now create disjoint clusters across the genes:\n- - Modify UPGMA to create disjoint clusters when the minimal distance is larger than a chosen threshold.\n - Show the disjoint clusters in the visualization by including separation after each cluster\n- Provide a way that allows the user to modify the threshold interactively\n- Could you manage to also separate the columns?\n- How about including the dendrogam?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"### Clustered Heatmap","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":216,"value":"$49","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":235,"value":"chartClustered.drawData(5)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":611,"value":"null","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":9,"value":"#### UPGMA","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":11,"value":"// Define the Cluster class\n class Cluster {\n constructor(label, size, members, data) {\n this.label = label;\n this.size = size;\n this.flat_children = members\n this.children = [];\n this.data_cluster = data\n this.distance_parent = 0\n }\n\n addChild(child, distance) {\n this.children.push(child);\n child.distance_parent = distance\n }\n }\n\n \n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"function upgma(data, threshold) {\n // Initialize clusters with individual data points\n const clusters = data.map((item, index) => new Cluster(item[0], 1, [item[0]], item[1]));\n // Calculate the pairwise distance matrix\n const distanceMatrix = calculateDistanceMatrix(clusters);\n // Run UPGMA on the given distance matrix\n return helper_upgma(distanceMatrix, threshold, clusters)\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":326,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":303,"value":"function updateDistanceMatrix(matrix, clusterIndices, clusters) {\n const [index1, index2] = clusterIndices;\n let clusterA = clusters[index1] \n let clusterB = clusters[index2] \n let last_row = []\n const newMatrix = [];\n let neededIndices = [...Array(matrix.length).keys()].filter(d => !clusterIndices.includes(d))\n for (let i = 0; i < neededIndices.length; i++) {\n newMatrix[i] = [];\n for (let j = 0; j < neededIndices.length; j++) {\n if (i === j) {\n newMatrix[i].push(0);\n } else {\n newMatrix[i].push(matrix[neededIndices[i]][neededIndices[j]]);\n }\n }\n let clustAtoI = matrix[neededIndices[i]][index1]\n let clustBtoI = matrix[neededIndices[i]][index2]\n let dist = (clusterA.size * clustAtoI + clusterB.size * clustBtoI) / (clusterA.size + clusterB.size)\n newMatrix[i].push(dist)\n last_row.push(dist)\n }\n last_row.push(0)\n newMatrix.push(last_row)\nreturn newMatrix \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":" function findMinDistance(matrix) {\n let minDistance = Infinity;\n let clusterIndices = [-1, -1];\n for (let i = 0; i < matrix.length; i++) {\n for (let j = i + 1; j < matrix[i].length; j++) {\n if (matrix[i][j] < minDistance) {\n minDistance = matrix[i][j];\n clusterIndices = [i, j];\n }\n }\n }\n return { minDistance, clusterIndices };\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":578,"value":"### Compute the distance matrix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":22,"value":" function calculateDistanceMatrix(clusters) {\n const distanceMatrix = [];\n for (let i = 0; i < clusters.length; i++) {\n distanceMatrix[i] = [];\n for (let j = 0; j < clusters.length; j++) {\n if (i === j) {\n distanceMatrix[i][j] = 0;\n } else {\n // Replace this with your distance calculation logic (e.g., Euclidean distance)\n distanceMatrix[i][j] = euclideanDistance(clusters[i].data_cluster, clusters[j].data_cluster);\n }\n }\n }\n return distanceMatrix;\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":43,"value":"function spearmanCorrelationDistance(arr1, arr2) {\n if (arr1.length !== arr2.length) {\n throw new Error(\"Input arrays must have the same length\");\n }\n\n const n = arr1.length;\n\n // Create rank arrays for both input arrays\n const rank1 = rankArray(arr1);\n const rank2 = rankArray(arr2);\n\n // Calculate the differences between the ranks\n const rankDiffSquared = rank1.map((r1, i) => Math.pow(r1 - rank2[i], 2));\n\n // Calculate Spearman's rank correlation coefficient\n const rho = 1 - (\n (6 * rankDiffSquared.reduce((sum, diffSquared) => sum + diffSquared, 0)) /\n (n * (n * n - 1)\n ));\n\n // The correlation distance is defined as 1 - Spearman's rank correlation coefficient\n const correlationDistance =1 - Math.abs(rho);\n\n return correlationDistance;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":266,"value":"function euclideanDistance(arr1, arr2) {\n if (arr1.length !== arr2.length) {\n throw new Error(\"Both arrays must have the same length.\");\n }\n\n let sumOfSquares = 0;\n\n for (let i = 0; i < arr1.length; i++) {\n const diff = arr1[i] - arr2[i];\n sumOfSquares += diff * diff;\n }\n\n return Math.sqrt(sumOfSquares);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":293,"value":"euclideanDistance([3, 4, 4, 6, 7, 14, 15], [9, 6, 6, 7, 6, 15, 19])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"function rankArray(arr) {\n // Create an array of indices and sort it based on the values in the input array\n const indices = [...arr.keys()];\n indices.sort((a, b) => arr[a] - arr[b]);\n\n // Create a rank array based on the sorted indices\n const rank = new Array(arr.length);\n for (let i = 0; i < indices.length; i++) {\n rank[indices[i]] = i + 1;\n }\n\n return rank;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":584,"value":"### For data preprocessing","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":224,"value":"function separateByGene(data){\n const perGene = {};\n for (let datum of data) {\n if (Object.keys(perGene).includes(datum.y)){\n perGene[datum.y].push(datum.value)\n }\n else {\n perGene[datum.y] = [datum.value]\n }\n }\n return Object.entries(perGene)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4b","stdlib":"1"}} 24:null