[{"data":1,"prerenderedAt":10539},["ShallowReactive",2],{"wrun-open-editor-url":3,"indicators:cookbook/skew-history":4},"https://openmarket.xyz/chart/#wrun-open=v1",{"slug":5,"filePath":6,"frontmatter":7,"rawMarkdown":12,"tree":13},"cookbook/skew-history","cookbook/skew-history.md",{"title":8,"description":9,"order":10,"section":11},"Skew history","How the chart's underlying's options skew has moved, and where today's term structure sits in its own past. Three reads. The 30-day 25 delta risk reversal, one…",151,"cookbook","---\ntitle: \"Skew history\"\ndescription: \"How the chart's underlying's options skew has moved, and where today's term structure sits in its own past. Three reads. The 30-day 25 delta risk reversal, one…\"\norder: 151\nsection: \"cookbook\"\n---\n\n\u003C!-- source: docs/indicators/cookbook/skew-history.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit -->\n\n# Skew history\n\nHow the chart's underlying's options skew has moved, and where today's term structure sits in its own past. Three reads. The 30-day 25 delta risk reversal, one per session from the daily options statistics (the call's IV minus the put's at the expiry nearest 30 days), drawn as a step line with its percentile and z-score against the window's earlier sessions. The risk reversal of one expiry, the one nearest the **Expiry, days out** setting, at 25 or 10 delta, read on every bar from the option surface, with each value checked against its present bit; a bar the data plane marks partial draws on a dotted line of its own and is counted, never mixed into the solid line. And the term structure now against its window: the at-the-money IV at seven constant maturities beside each one's median and 25th and 75th percentile over the window's sessions, in a panel below the chart. A card at the bottom right names the skew (puts rich when the put IV minus the call IV is over 0.06 of the 30-day IV, calls rich below 0, flat between) with the numbers behind it.\n\nThe parts are scalar `option_daily` inputs and the celled `option_surface` source ([Option surface](../core-concepts/data-sources.md#option-surface)) read through `hasBit` and `isPartial`, the options kit's `DayHistory` for the percentile, the z-score and the quantiles ([Options kit](../functions/options-kit.md#a-history-of-daily-statistics)), a `panel.line` over category maturities ([Line panels](../presentation/cards-frames-panels.md#line-panels)), and a `render.hud` card. This is also the `skew-history` template: the **Skew History** card under **Beyond the time axis** in the editor's starter list, and it compiles as written.\n\n## The wrun indicator\n\n```typescript sample=skew-history\n// Skew History: how the chart's underlying's options skew has moved, and where today's term structure sits in its own\n// past. Three reads. The 30-day 25 delta risk reversal, one per session from the daily options statistics\n// (option_daily: the call's IV minus the put's at the expiry nearest 30 days), drawn as a step line with its percentile\n// and z-score against the window's earlier sessions. The risk reversal of one expiry, the one nearest the Expiry\n// setting's days out, at 25 or 10 delta, read on every bar from the option surface (option_surface: one tuple per\n// expiry with present bits per value; a bar the data plane marks partial, bit 14, draws on a dotted line of its own\n// and is counted, never mixed into the solid line). And the term structure now against its window: the at-the-money\n// IV at seven constant maturities (7 days to a year) beside each one's median and 25th and 75th percentile over the\n// window's sessions, in a panel below the chart. A card at the bottom right names the skew (puts rich over 0.06 of\n// the 30-day IV, calls rich below 0, flat between) with the numbers behind it. The statistics are short today (they\n// start when the data plane switches the daily job on): the percentile, the z-score and the distribution need Minimum\n// history (60 sessions), and until then the card says how many sessions there are. The surface's five-minute history\n// is kept 30 days, so older intraday bars arrive partial. US stock charts, daily or finer.\n\nparam.int(\"days\", 30, { min: 1, max: 365, label: \"Expiry, days out\", description: \"The surface line reads the expiry nearest this many days out (never one that settles today)\" });\nparam.choice(\"delta\", [\"25 delta\", \"10 delta\"], \"25 delta\", { label: \"Surface delta\", description: \"The wings the surface line compares: 25 delta, or 10 delta further out\" });\nparam.int(\"lookback\", 252, { min: 20, max: 520, label: \"Window, sessions\", description: \"Sessions the percentile, the z-score and the term distribution read: 252 is about a year\" });\nparam.int(\"min_sessions\", 60, { min: 10, max: 520, label: \"Minimum history, sessions\", description: \"Sessions of statistics before the percentile, the z-score and the distribution show\" });\ninput(\"close\", ohlcv.close); // the chart's own close: the grid\ninput(\"rr25\", option_daily.rr25_30d, { missing: \"nan\", description: \"The 30-day 25 delta risk reversal, call IV minus put IV, volatility points, one row per session\" });\ninput(\"iv7\", option_daily.atm_iv_7d, { missing: \"nan\", description: \"The 7-day at-the-money IV, percent\" });\ninput(\"iv14\", option_daily.atm_iv_14d, { missing: \"nan\", description: \"The 14-day at-the-money IV, percent\" });\ninput(\"iv30\", option_daily.atm_iv_30d, { missing: \"nan\", description: \"The 30-day at-the-money IV, percent\" });\ninput(\"iv60\", option_daily.atm_iv_60d, { missing: \"nan\", description: \"The 60-day at-the-money IV, percent\" });\ninput(\"iv90\", option_daily.atm_iv_90d, { missing: \"nan\", description: \"The 90-day at-the-money IV, percent\" });\ninput(\"iv180\", option_daily.atm_iv_180d, { missing: \"nan\", description: \"The 180-day at-the-money IV, percent\" });\ninput(\"iv365\", option_daily.atm_iv_365d, { missing: \"nan\", description: \"The 365-day at-the-money IV, percent\" });\ninput(\"surface\", option_surface.cells, { max_cells: 1800, description: \"The underlying's option surface on the bar: one tuple per expiry\" }); // [expiry_ms, dte_days, forward, atm_iv, iv_p25, iv_c25, iv_p10, iv_c10, present] per expiry\noutput(\"rr30\", line, lower, { color: \"#38bdf8\", width: 2, step: true, label: \"RR 30d\", format: \"0.00\", description: \"The 30-day 25 delta risk reversal, call IV minus put IV, volatility points, per session\" });\noutput(\"rr_expiry\", line, lower, { color: \"#f59e0b\", width: 1, label: \"RR expiry\", format: \"0.00\", description: \"The chosen expiry's risk reversal at the chosen delta, call IV minus put IV, volatility points, per bar\" });\noutput(\"rr_partial\", line, lower, { color: \"#64748b\", width: 1, line_style: \"dotted\", label: \"RR partial\", format: \"0.00\", description: \"The same reading on a bar the data plane marks partial: a floor of the data, never the solid line\" });\noutput(\"zero\", line, lower, { role: \"guide\", color: \"#475569\", label: \"0\", description: \"The zero line: below it puts are dearer than calls\" });\noutput(\"rr_pct\", none, lower, { description: \"The newest 30-day risk reversal's percentile among the window's earlier sessions, 0 to 100\" });\noutput(\"rr_z\", none, lower, { description: \"The newest 30-day risk reversal against the mean and deviation of the window's earlier sessions\" });\noutput(\"scaled\", none, lower, { description: \"Put IV minus call IV over the 30-day IV (the risk reversal turned round and scaled): the skew word's number\" });\noutput(\"skew_code\", none, lower, { description: \"0 calls rich (scaled under 0), 1 flat, 2 puts rich (scaled over 0.06); 1 with no reading\" });\noutput(\"expiry_days\", none, lower, { description: \"Days to the expiry the surface line reads\" });\noutput(\"partial_bars\", none, lower, { description: \"Bars so far whose surface the data plane marked partial\" });\noutput(\"sessions\", none, lower, { description: \"Sessions of statistics the window holds\" });\noutput(\"status\", none, lower, { description: \"0 not enough history yet, 1 the window reads, 2 a chart coarser than a day\" });\nstring(\"read\", { max_bytes: 64 }); // the headline\nstring(\"title\", { max_bytes: 64 }); // the card's title\nstring(\"history_text\", { max_bytes: 48 }); // \"Percentile 18, z -1.42\" or the wait\nconst termRows = frame(\"term_rows\", { max_bytes: 4096 }); // one row per maturity: [label, now, median, 25th, 75th]\n// The term structure now against its window: the maturities across, IV up; the frame carries the caption per run.\npanel.line({ name: \"term\", title: \"Term structure against its window\", x: \"category\", place: \"below\", frame: termRows, height_frac: 0.24, chrome: \"grid\", hover_card: true, legend_style: \"chips\", format: \"0.0\", unit: \"%\", y_title: \"At-the-money IV\", series: [\n  { name: \"Now\", color: \"#e2e8f0\", width: 2.5, points: true },\n  { name: \"Median\", color: \"#38bdf8\", width: 1.5 },\n  { name: \"25th\", color: \"#64748b\", width: 1, line_style: \"dashed\" },\n  { name: \"75th\", color: \"#64748b\", width: 1, line_style: \"dashed\" },\n] });\n\nrender.hud(\"skew_card\", {\n  position: \"bottom_right\",\n  look: \"terminal\",\n  title: \"{{title}}\",\n  columns: 2,\n  tiles: [\n    tile.pill(\"Skew\", \"read\", { headline: true, color_by: \"skew_code\", colors: [\"#38bdf8\", \"#94a3b8\", \"#a78bfa\"] }),\n    tile.pill(\"Against its history\", \"history_text\", { color_by: \"status\", colors: [\"#94a3b8\", \"#e2e8f0\", \"#94a3b8\"] }),\n    tile.value(\"RR 30d\", \"rr30\", { format: \"0.00\" }),\n    tile.rows([\n      [\"1) RR, chosen expiry\", \"rr_expiry\", \"0.00\"],\n      [\"2) Expiry, days out\", \"expiry_days\", \"int\"],\n      [\"3) Skew over IV\", \"scaled\", \"0.000\"],\n      [\"4) Percentile\", \"rr_pct\", \"0\"],\n      [\"5) Z-score\", \"rr_z\", \"0.00\"],\n      [\"6) Partial bars\", \"partial_bars\", \"int\"],\n    ]),\n  ],\n});\n\nconst DAY = 86400.0;\nconst TUPLE = 9; // option_surface: expiry_ms, dte_days, forward, atm_iv, iv_p25, iv_c25, iv_p10, iv_c10, present\nconst BIT_DTE = 1; // present bits: each value after expiry_ms, then the partial bar\nconst BIT_P25 = 4;\nconst BIT_C25 = 5;\nconst BIT_P10 = 6;\nconst BIT_C10 = 7;\nconst PUT_RICH = 0.06; // the scaled skew past which puts are rich (under 0, calls are)\nconst CAPACITY = 520;\nconst TENORS = 7;\nconst TENOR_LABELS: String[] = [\"7d\", \"14d\", \"30d\", \"60d\", \"90d\", \"180d\", \"1y\"];\nconst MONTHS: String[] = [\"JAN\", \"FEB\", \"MAR\", \"APR\", \"MAY\", \"JUN\", \"JUL\", \"AUG\", \"SEP\", \"OCT\", \"NOV\", \"DEC\"];\nconst rrs = new DayHistory(CAPACITY); // one 30-day risk reversal per session\nconst terms: DayHistory[] = []; // one history per maturity\nfor (let k = 0; k \u003C TENORS; k += 1) terms.push(new DayHistory(CAPACITY));\nconst termNow = new StaticArray\u003Cf64>(TENORS); // the newest session's IV per maturity\nconst dateClock = new Clock(\"UTC\");\n\nlet targetDays = 30.0; // settings, read in onStart()\nlet tenDelta = false;\nlet lookback = 252;\nlet need = 60;\nlet prevT: f64 = NaN; // the bar spacing\nlet barSec: f64 = NaN;\nlet rrNow: f64 = NaN; // the session readings, held\nlet pctNow: f64 = NaN;\nlet zNow: f64 = NaN;\nlet scaledNow: f64 = NaN;\nlet iv30Now: f64 = NaN;\nlet partialBars = 0;\nlet lastDays: f64 = NaN; // the surface line's expiry, held for the card\n\nfunction onStart(): void {\n  targetDays = p_days();\n  tenDelta = i32(p_delta()) == 1;\n  lookback = i32(p_lookback());\n  need = i32(p_min_sessions());\n  if (need > lookback) need = lookback;\n  for (let k = 0; k \u003C TENORS; k += 1) termNow[k] = NaN;\n}\n\nfunction tenorInput(k: i32): f64 {\n  if (k == 0) return in_iv7();\n  if (k == 1) return in_iv14();\n  if (k == 2) return in_iv30();\n  if (k == 3) return in_iv60();\n  if (k == 4) return in_iv90();\n  if (k == 5) return in_iv180();\n  return in_iv365();\n}\n\n// ── The surface on this bar: the expiry nearest targetDays with both wings served, and whether the bar is partial ──\nlet surfaceRr: f64 = NaN;\nlet surfaceDays: f64 = NaN;\nlet surfacePartial = false;\nfunction readSurface(): void {\n  surfaceRr = NaN;\n  surfaceDays = NaN;\n  surfacePartial = false;\n  const n = in_surface_cells();\n  if (n \u003C TUPLE) return; // an empty bar: no surface, a gap in the line\n  const cells = in_surface_view();\n  const putBit = tenDelta ? BIT_P10 : BIT_P25;\n  const callBit = tenDelta ? BIT_C10 : BIT_C25;\n  const putAt = tenDelta ? 6 : 4;\n  const callAt = tenDelta ? 7 : 5;\n  let bestGap: f64 = Infinity;\n  let bestExpiry: f64 = Infinity;\n  for (let i = 0; i + TUPLE \u003C= n; i += TUPLE) {\n    const present = cells[i + 8];\n    if (isPartial(present)) surfacePartial = true;\n    if (!hasBit(present, BIT_DTE) || !hasBit(present, putBit) || !hasBit(present, callBit)) continue;\n    const dte = cells[i + 1];\n    if (!(dte >= 1.0)) continue; // an expiry that settles today never stands for a tenor\n    const gap = Math.abs(dte - targetDays);\n    const expiry = cells[i];\n    if (gap \u003C bestGap || (gap == bestGap && expiry \u003C bestExpiry)) {\n      bestGap = gap;\n      bestExpiry = expiry;\n      surfaceDays = dte;\n      surfaceRr = cells[i + callAt] - cells[i + putAt];\n    }\n  }\n}\n\n// ── The session readings, when a session lands ──\nfunction measure(): void {\n  rrNow = rrs.value(0);\n  const ready = rrs.span(lookback) >= need;\n  pctNow = ready ? rrs.percentile(lookback) : NaN;\n  zNow = ready ? rrs.zscore(lookback) : NaN;\n  scaledNow = iv30Now > 0.0 ? -rrNow / iv30Now : NaN;\n}\n\nfunction skewCode(): f64 {\n  if (isNaN(scaledNow)) return 1.0;\n  return scaledNow > PUT_RICH ? 2.0 : scaledNow \u003C 0.0 ? 0.0 : 1.0;\n}\n\nfunction sbDay(day: f64): void { // \"16OCT\"\n  dateClock.update(day * DAY);\n  if (dateClock.dayOfMonth() \u003C 10) sb_text(\"0\");\n  sb_int(dateClock.dayOfMonth());\n  sb_text(MONTHS[dateClock.month() - 1]);\n}\n\nfunction sbSigned(v: f64): void { // \"+1.20\", \"-4.05\"\n  if (v >= 0.0) sb_text(\"+\");\n  sb_f64(v, 2);\n}\n\n// ── The term panel: each maturity now, its median and quartiles over the window ──\nfunction writeTerm(): void {\n  fb_clear();\n  fb_text(\"{\\\"rows\\\":[\");\n  for (let k = 0; k \u003C TENORS; k += 1) {\n    if (k > 0) fb_text(\",\");\n    fb_text(\"[\");\n    fb_str(TENOR_LABELS[k]);\n    const h = terms[k];\n    const ready = h.span(lookback) >= need;\n    const now = termNow[k];\n    fb_text(\",\");\n    if (isNaN(now)) fb_text(\"null\");\n    else fb_f64(now, 2);\n    for (let q = 0; q \u003C 3; q += 1) {\n      fb_text(\",\");\n      const v = ready ? h.quantile(lookback, q == 0 ? 0.5 : q == 1 ? 0.25 : 0.75) : NaN;\n      if (isNaN(v)) fb_text(\"null\");\n      else fb_f64(v, 2);\n    }\n    fb_text(\"]\");\n  }\n  fb_text(\"],\\\"caption\\\":\\\"\");\n  const held = terms[2].span(lookback);\n  if (held \u003C need) {\n    fb_text(\"Not enough history yet: \");\n    fb_int(held);\n    fb_text(\" of \");\n    fb_int(need);\n    fb_text(\" sessions\");\n  } else {\n    fb_text(\"Now against \");\n    fb_int(held);\n    fb_text(\" sessions\");\n  }\n  fb_text(\"\\\"}\");\n  writeFrameBuffer(FRAME_TERM_ROWS);\n}\n\nfunction writeWords(coarse: bool): void {\n  const held = rrs.span(lookback);\n  sb_clear();\n  if (coarse) sb_text(\"Needs a daily or finer chart\");\n  else if (rrs.count() == 0) sb_text(\"Waiting for the daily options statistics\");\n  else {\n    const code = skewCode();\n    sb_text(code == 2.0 ? \"Puts rich, RR \" : code == 0.0 ? \"Calls rich, RR \" : \"Skew flat, RR \");\n    sbSigned(rrNow);\n  }\n  str_read_sb();\n  sb_clear();\n  if (coarse || rrs.count() == 0) sb_text(\"No history\");\n  else if (held \u003C need) {\n    sb_text(\"Not enough history yet: \");\n    sb_int(held);\n    sb_text(\" of \");\n    sb_int(need);\n    sb_text(\" sessions\");\n  } else {\n    sb_text(\"Percentile \");\n    sb_f64(pctNow, 0);\n    if (!isNaN(zNow)) {\n      sb_text(\", z \");\n      sbSigned(zNow);\n    }\n  }\n  str_history_text_sb();\n  sb_clear();\n  sb_text(\"Skew history, 25 delta\");\n  if (!coarse && rrs.count() > 0) {\n    sb_text(\", as of \");\n    sbDay(rrs.day(0));\n  }\n  str_title_sb();\n}\n\n// onBar() runs once per bar: the spacing; the surface's expiry on every bar; the session's statistics when they land\n// (the risk reversal and each maturity's IV). Each bar writes the held session readings beside its own surface line.\nfunction onBar(): void {\n  const t = bar.time();\n  if (!isNaN(prevT) && t > prevT && (isNaN(barSec) || t - prevT \u003C barSec)) barSec = t - prevT;\n  prevT = t;\n  const coarse = !isNaN(barSec) && barSec > 1.5 * DAY;\n  readSurface();\n  if (surfacePartial) partialBars += 1;\n  if (!isNaN(surfaceDays)) lastDays = surfaceDays;\n  const day = Math.floor(t / DAY);\n  if (!coarse) {\n    const iv30 = in_iv30();\n    if (!isNaN(iv30) && iv30 > 0.0) iv30Now = iv30;\n    for (let k = 0; k \u003C TENORS; k += 1) {\n      const v = tenorInput(k);\n      if (!isNaN(v) && v > 0.0 && terms[k].push(day, v)) termNow[k] = v;\n    }\n    const rr = in_rr25();\n    if (!isNaN(rr) && rrs.push(day, rr)) measure();\n  }\n  out_zero(0.0);\n  out_rr30(coarse ? NaN : rrNow);\n  out_rr_expiry(coarse || surfacePartial ? NaN : surfaceRr);\n  out_rr_partial(!coarse && surfacePartial ? surfaceRr : NaN);\n  out_rr_pct(coarse ? NaN : pctNow);\n  out_rr_z(coarse ? NaN : zNow);\n  out_scaled(coarse ? NaN : scaledNow);\n  out_skew_code(coarse ? 1.0 : skewCode());\n  out_expiry_days(coarse ? NaN : lastDays);\n  out_partial_bars(f64(partialBars));\n  out_sessions(coarse ? NaN : f64(rrs.span(lookback)));\n  out_status(coarse ? 2.0 : rrs.span(lookback) >= need ? 1.0 : 0.0);\n  if (bar.isLast()) {\n    writeWords(coarse);\n    if (!coarse) writeTerm();\n  }\n}\n```\n\n## How it works\n\n**The session line.** `rr25_30d` is the statistics' 30-day risk reversal, call IV minus put IV in volatility points: below zero the puts are dearer, the usual shape on a stock. Each session's reading joins a `DayHistory`; `percentile()` and `zscore()` read it against the window's earlier sessions.\n\n**The surface line.** Every bar's `option_surface` block holds one tuple per expiry, `[expiry_ms, dte_days, forward, atm_iv, iv_p25, iv_c25, iv_p10, iv_c10, present]`. The module keeps the expiry whose `dte_days` is nearest the setting among those whose days and both wings are present (bits 1, 4 and 5 at 25 delta, bits 1, 6 and 7 at 10 delta), never an expiry that settles that day, and draws its call wing minus its put wing. When the nearest expiry lacks a wing the next nearest stands in. A bar with bit 14 set on any tuple is partial (older than the five-minute history the data plane keeps, or cut short): its reading goes to the dotted **RR partial** line, a floor of the data rather than a value.\n\n**The term panel.** Each maturity's IV joins its own `DayHistory`; on the live bar `quantile()` reads the median and the quartiles over the window, and the panel draws them beside the newest session's curve.\n\n## Where it runs\n\nUS stock charts, through OpenMarket's official package: the chart's browser lane serves `option_daily` for the chart's own underlying ([Limitations](../reference/limitations.md)). It is declared ahead of the lane that serves it, so the template builds today and the chart shows the lane's refusal until the data plane serves it. The surface line reads `option_surface`, which the chart's browser lane serves on crypto, CME and US stock charts ([Option surface](../core-concepts/data-sources.md#option-surface)). A daily or finer chart: the daily surface has no retention limit, the five-minute one keeps 30 days.\n\n## When data is missing\n\nThe statistics start the day their job is switched on. The session line reads from the first session; the percentile, the z-score and the term distribution need **Minimum history** (60 sessions), and until then the pill and the panel's caption read \"Not enough history yet: 12 of 60 sessions\". A bar with no surface block draws nothing on either surface line; the card keeps the expiry it last read. Before the first session the card reads \"Waiting for the daily options statistics\"; a chart coarser than a day reads \"Needs a daily or finer chart\".\n\n## Customize it\n\n- **Another expiry.** Set **Expiry, days out** to 7 for the weekly or 90 for the quarter.\n- **Further wings.** Switch **Surface delta** to 10 delta to read the tails.\n- **Another year.** `lookback` sets the sessions the percentile, the z-score and the distribution read.\n\n## Run it\n\n1. In the editor's Explorer, press the **Templates** icon and pick **Skew History** under **Beyond the time axis**.\n2. Press **Run** on a US stock's chart: the session line and the surface line fill as the statistics allow.\n3. At the editor's Console prompt, type `rr30`, `rr_pct` and `partial_bars`.\n\n## Concepts used\n\n- [Option surface](../core-concepts/data-sources.md#option-surface) for `option_surface` on crypto, CME and US stock charts, and [The present mask and partial bars](../core-concepts/data-sources.md#the-present-mask-and-partial-bars) for its present mask and the partial bar\n- [Data sources](../core-concepts/data-sources.md#us-listed-options-by-the-charts-underlying) for `option_daily`\n- [Options kit](../functions/options-kit.md#a-history-of-daily-statistics) for `DayHistory`\n- [Line panels](../presentation/cards-frames-panels.md#line-panels) for the term panel\n",{"type":14,"children":15,"data":10532,"position":10534},"root",[16,26,29,30,72,73,371,372,389,390,9436,9437,9453,9454,9562,9563,9675,9676,9743,9744,9760,9761,9862,9863,9879,9880,9918,9919,9934,9935,10102,10103,10119,10120,10324,10325,10340,10341],{"type":17,"value":18,"position":19},"comment"," source: docs/indicators/cookbook/skew-history.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit ",{"start":20,"end":23},{"line":21,"column":21,"offset":22},1,0,{"line":21,"column":24,"offset":25},128,127,{"type":27,"value":28},"text","\n",{"type":27,"value":28},{"type":31,"tagName":32,"properties":33,"children":34,"position":69},"element","p",{},[35,44,62],{"type":27,"value":36,"position":37},"How the chart's underlying's options skew has moved, and where today's term structure sits in its own past. Three reads. The 30-day 25 delta risk reversal, one per session from the daily options statistics (the call's IV minus the put's at the expiry nearest 30 days), drawn as a step line with its percentile and z-score against the window's earlier sessions. 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