From f508bfaaf8a96f765c4c2bf1c3d5a22880a43a2f Mon Sep 17 00:00:00 2001 From: Ulzii Otgonbaatar Date: Mon, 23 Feb 2026 15:01:58 -0700 Subject: [PATCH 1/5] Add plan for humanizing all computer interaction endpoints Covers click, type, press key, scroll, and drag mouse with performance-first algorithms (zero additional xdotool process spawns). Includes the existing Bezier curve mouse movement as reference. Co-authored-by: Cursor --- plans/humanize-computer-endpoints.md | 210 +++++++++++++++++++++++++++ 1 file changed, 210 insertions(+) create mode 100644 plans/humanize-computer-endpoints.md diff --git a/plans/humanize-computer-endpoints.md b/plans/humanize-computer-endpoints.md new file mode 100644 index 00000000..2eb8962c --- /dev/null +++ b/plans/humanize-computer-endpoints.md @@ -0,0 +1,210 @@ +# Humanize All Computer Interaction Endpoints + +> Add human-like behavior to all computer interaction API endpoints using fast, pre-computed algorithms that add zero additional xdotool process spawns. + +## Performance-First Design Principle + +**The bottleneck is xdotool process spawns** (fork+exec per call), not Go-side computation. Every algorithm below is designed around two rules: + +1. **One xdotool call per API request** -- pre-compute all timing in Go and bake it into a single chained xdotool command with inline `sleep` directives. This is the same pattern already used by `doDragMouse` (see lines 911-951 of `computer.go`). +2. **O(1) or O(n) math only** -- uniform random (`rand.Intn`), simple easing polynomials (2-3 multiplies), no lookup tables, no transcendental functions beyond what `mousetrajectory.go` already uses. + +```mermaid +flowchart LR + Go["Go: pre-compute timing array O(n)"] --> Args["Build xdotool arg slice"] + Args --> OneExec["Single fork+exec"] + OneExec --> Done["Done"] +``` + + + +### Existing proof this works + +`doDragMouse` already chains `mousemove_relative dx dy sleep 0.050 mousemove_relative dx dy sleep 0.050 ...` in a single xdotool invocation. Every strategy below follows this exact pattern. + +--- + +## 0. Move Mouse -- Bezier Curve Trajectory (Already Implemented) + +**Status:** Complete. This is the reference implementation that all other endpoints follow. + +**Cost:** N xdotool calls (one `mousemove_relative` per trajectory point) with Go-side sleeps. Typically 5-80 steps depending on distance. + +**Algorithm:** Bezier curve with randomized control points, distortion, and easing. Ported from Camoufox/HumanCursor. + +- **Bezier curve**: 2 random internal knots within an 80px-padded bounding box around start/end. Bernstein polynomial evaluation produces smooth curved path. O(n) computation. +- **Distortion**: 50% chance per interior point to apply Gaussian jitter (mean=1, stdev=1 via Box-Muller transform). Adds micro-imperfections. +- **Easing**: `easeOutQuad(t) = -t*(t-2)` -- cursor decelerates as it approaches the target, matching natural human behavior. +- **Point count**: Auto-computed from path length (`pathLength^0.25 * 20`), clamped to [5, 80]. Override via `Options.MaxPoints`. +- **Per-step timing**: ~10ms default step delay with +/-2ms uniform jitter. When `duration_ms` is specified, delay is computed as `duration_ms / numSteps`. +- **Screen clamping**: Trajectory points clamped to screen bounds to prevent X11 delta accumulation errors. + +**Key files:** + +- `[server/lib/mousetrajectory/mousetrajectory.go](kernel-images/server/lib/mousetrajectory/mousetrajectory.go)` -- Bezier curve generation (~230 lines) +- `[server/cmd/api/api/computer.go](kernel-images/server/cmd/api/api/computer.go)` lines 104-206 -- `doMoveMouseSmooth` integration + +**API (existing):** `MoveMouseRequest` has `smooth: boolean` (default `true`) and optional `duration_ms` (50-5000ms). + +**Implementation in `doMoveMouseSmooth`:** + +1. Get current mouse position via `xdotool getmouselocation` +2. Generate Bezier trajectory: `mousetrajectory.NewHumanizeMouseTrajectoryWithOptions(fromX, fromY, toX, toY, opts)` +3. Clamp points to screen bounds +4. For each point: `xdotool mousemove_relative -- dx dy`, then `sleepWithContext` with jittered delay +5. Modifier keys held via `keydown`/`keyup` wrapper + +**Note:** This endpoint uses per-step Go-side sleeps (not xdotool inline `sleep`) because the trajectory includes screen-clamping logic that adjusts deltas at runtime. The other endpoints below use inline `sleep` since their timing can be fully pre-computed. + +--- + +## Shared Library: `server/lib/humanize/humanize.go` + +Tiny utility package (no external deps, no data structures) providing: + +```go +// UniformJitter returns a random duration in [base-jitter, base+jitter], clamped to min. +func UniformJitter(rng *rand.Rand, baseMs, jitterMs, minMs int) time.Duration + +// EaseOutQuad computes t*(2-t) for t in [0,1]. Two multiplies. +func EaseOutQuad(t float64) float64 + +// SmoothStepDelay maps position i/n through a smoothstep curve to produce +// a delay in [fastMs, slowMs]. Used for scroll and drag easing. +// smoothstep(t) = 3t^2 - 2t^3. Three multiplies. +func SmoothStepDelay(i, n, slowMs, fastMs int) time.Duration + +// FormatSleepArg formats a duration as a string suitable for xdotool's +// inline sleep command (e.g. "0.085"). Avoids fmt.Sprintf per call. +func FormatSleepArg(d time.Duration) string +``` + +All functions are pure, allocate nothing, and cost a few arithmetic ops each. Tested with table-driven tests and deterministic seeds. + +--- + +## 1. Click Mouse -- Single-Call Down/Sleep/Up + +**Cost:** 1 xdotool call (same as current). Pre-computation: 1-2 `rand.Intn` calls. + +**Algorithm:** Replace `click` with `mousedown sleep mouseup ` in the same xdotool arg slice. No separate process spawns. + +- **Dwell time**: `UniformJitter(rng, 90, 30, 50)` -> range [60, 120]ms. This matches measured human click dwell without needing lognormal sampling. +- **Micro-drift**: Append `mousemove_relative ` between mousedown and mouseup, where dx/dy are `rand.Intn(3)-1` (range [-1, 1] pixels). Trivially cheap. +- **Multi-click**: For `num_clicks > 1`, loop and insert inter-click gaps via `UniformJitter(rng, 100, 30, 60)` -> [70, 130]ms. + +**Single xdotool call example:** + +``` +xdotool mousemove 500 300 mousedown 1 sleep 0.085 mousemove_relative -- 1 0 mouseup 1 +``` + +**API change:** Add `smooth: boolean` (default `true`) to `ClickMouseRequest`. + +--- + +## 2. Type Text -- Chunked Type with Inter-Word Pauses + +**Cost:** 1 xdotool call (same as current). Pre-computation: O(words) random samples. + +**Algorithm:** Instead of per-character keysym mapping (which is complex and fragile for Unicode), split text by whitespace/punctuation into chunks and chain `xdotool type --delay "chunk" sleep ` commands. + +- **Intra-word delay**: Per-chunk, pick `rand.Intn(70) + 50` -> [50, 120]ms. Varies per chunk to simulate burst-pause rhythm. +- **Inter-word pause**: Between chunks, insert `sleep` with `UniformJitter(rng, 140, 60, 60)` -> [80, 200]ms. Longer pauses at sentence boundaries (after `.!?`): multiply by 1.5x. +- **No bigram tables**: The per-word delay variation is sufficient for convincing humanization. Bigram-level precision adds complexity with diminishing returns for bot detection evasion. + +**Single xdotool call example:** + +``` +xdotool type --delay 80 -- "Hello" sleep 0.150 type --delay 65 -- " world" sleep 0.300 type --delay 95 -- ". How" sleep 0.120 type --delay 70 -- " are" sleep 0.140 type --delay 85 -- " you?" +``` + +**API change:** Add `smooth: boolean` (default `false`) to `TypeTextRequest`. When `smooth=true`, the existing `delay` field is ignored. + +**Why this is fast:** We never leave the `xdotool type` mechanism (which handles Unicode, XKB keymaps, etc. internally). We just break it into chunks with sleeps between them. One fork+exec total. + +--- + +## 3. Press Key -- Dwell via Inline Sleep + +**Cost:** 1 xdotool call (same as current). Pre-computation: 1 `rand.Intn` call. + +**Algorithm:** Replace `key ` with `keydown sleep keyup `. + +- **Tap dwell**: `UniformJitter(rng, 95, 30, 50)` -> [65, 125]ms. +- **Modifier stagger**: When `hold_keys` are present, insert a small `sleep 0.025` between each `keydown` for modifiers, then the primary key sequence. Release in reverse order with the same stagger. This costs zero extra xdotool calls -- it's all in the same arg slice. + +**Single xdotool call example (Ctrl+C):** + +``` +xdotool keydown ctrl sleep 0.030 keydown c sleep 0.095 keyup c sleep 0.025 keyup ctrl +``` + +**API change:** Add `smooth: boolean` (default `false`) to `PressKeyRequest`. + +--- + +## 4. Scroll -- Eased Tick Intervals in One Call + +**Cost:** 1 xdotool call (same as current). Pre-computation: O(ticks) easing function evaluations (3 multiplies each). + +**Algorithm:** Replace `click --repeat N --delay 0 ` with N individual `click ` commands separated by pre-computed `sleep` values following a **smoothstep easing curve**. + +- **Easing**: `SmoothStepDelay(i, N, slowMs=80, fastMs=15)` for each tick i. The smoothstep `3t^2 - 2t^3` creates natural momentum: slow start, fast middle, slow end. +- **Jitter**: Add `rand.Intn(10) - 5` ms to each delay. Trivially cheap. +- **Small scrolls (1-3 ticks)**: Skip easing, use uniform delay of `rand.Intn(40) + 30` ms. + +**Single xdotool call example (5 ticks down):** + +``` +xdotool mousemove 500 300 click 5 sleep 0.075 click 5 sleep 0.035 click 5 sleep 0.018 click 5 sleep 0.040 click 5 +``` + +**API change:** Add `smooth: boolean` (default `false`) to `ScrollRequest`. + +**Why not per-tick Go-side sleeps?** That would require N separate xdotool calls (N fork+execs). Inline `sleep` achieves the same timing in one process. + +--- + +## 5. Drag Mouse -- Bezier Path + Eased Delays + +**Cost:** Same as current (1-3 xdotool calls for the 3 phases). Pre-computation: Bezier generation (already proven fast in `mousetrajectory.go`). + +**Algorithm:** When `smooth=true`, auto-generate the drag path using the existing `mousetrajectory.HumanizeMouseTrajectory` Bezier library, then apply eased step delays (instead of the current fixed `step_delay_ms`). + +- **Path generation**: `mousetrajectory.NewHumanizeMouseTrajectoryWithOptions(startX, startY, endX, endY, opts)` -- already O(n) with Bernstein polynomial evaluation. Proven fast. +- **Eased step delays**: Replace the fixed `stepDelaySeconds` in the Phase 2 xdotool chain with per-step delays from `SmoothStepDelay`. Slow at start (pickup) and end (placement), fast in middle. These are already baked into the single xdotool arg slice, so zero extra process spawns. +- **Jitter**: Same `rand.Intn(5) - 2` ms pattern already used by `doMoveMouseSmooth`. + +**API change:** Add `smooth: boolean` (default `false`) to `DragMouseRequest`. When `smooth=true` and `path` has exactly 2 points (start + end), the server generates a Bezier curve between them and replaces `path` with the generated waypoints. + +**No new `start`/`end` fields needed** -- the caller simply provides `path: [[startX, startY], [endX, endY]]` and the server expands it. + +--- + +## Computational Cost Summary + + +| Endpoint | xdotool calls | Pre-computation | Algorithm | +| ------------- | ---------------- | --------------------------------- | ------------------------------------ | +| `move_mouse` | O(points) (done) | O(points) Bezier + Box-Muller | Bezier curve + easeOutQuad + jitter | +| `click_mouse` | 1 (same) | 1-2x `rand.Intn` | Uniform random dwell | +| `type_text` | 1 (same) | O(words) `rand.Intn` | Chunked type + inter-word sleep | +| `press_key` | 1 (same) | 1x `rand.Intn` | Inline keydown/sleep/keyup | +| `scroll` | 1 (same) | O(ticks) smoothstep (3 muls each) | Eased inter-tick sleep | +| `drag_mouse` | 1-3 (same) | O(points) Bezier (existing) | Bezier path + smoothstep step delays | + + +No additional process spawns. No heap allocations beyond the existing xdotool arg slice. No lookup tables. Every random sample is a single `rand.Intn` or `rand.Float64` call. + +--- + +## Files to Create/Modify + +- **Modify:** `[server/openapi.yaml](kernel-images/server/openapi.yaml)` -- Add `smooth` boolean to 5 request schemas +- **Modify:** `[server/cmd/api/api/computer.go](kernel-images/server/cmd/api/api/computer.go)` -- Add humanized code paths (branching on `smooth` flag) +- **Create:** `server/lib/humanize/humanize.go` -- Shared primitives (~50 lines) +- **Create:** `server/lib/humanize/humanize_test.go` -- Table-driven tests +- **Regenerate:** OpenAPI-generated types (run code generation after schema changes) + +No separate per-endpoint library packages needed. The shared `humanize` package plus the existing `mousetrajectory` package cover everything. \ No newline at end of file From 86e3a10785917f6d5d2b42bedadfe0cac5ca07cd Mon Sep 17 00:00:00 2001 From: Ulzii Otgonbaatar Date: Wed, 4 Mar 2026 08:30:42 -0700 Subject: [PATCH 2/5] feat: add smooth Bezier movement support to dragMouse - Add smooth (boolean, default false) and duration_ms (integer, 50-10000ms) to DragMouseRequest in OpenAPI spec - Add GenerateMultiSegmentTrajectory to mousetrajectory library: chains per-pair Bezier curves with proportional point distribution and screen bounds clamping - Refactor doDragMouse into doDragMouseLinear (existing behavior) and doDragMouseSmooth (Bezier path with jitter delays) - Add multi-segment trajectory tests and visual demo script Made-with: Cursor --- images/chromium-headful/test_smooth_drag.py | 194 ++++++++++++ server/api | Bin 13985442 -> 14040034 bytes server/cmd/api/api/computer.go | 101 +++++- server/lib/mousetrajectory/mousetrajectory.go | 107 +++++++ .../mousetrajectory/mousetrajectory_test.go | 68 ++++ server/lib/oapi/oapi.go | 295 +++++++++--------- server/openapi.yaml | 13 +- 7 files changed, 615 insertions(+), 163 deletions(-) create mode 100644 images/chromium-headful/test_smooth_drag.py diff --git a/images/chromium-headful/test_smooth_drag.py b/images/chromium-headful/test_smooth_drag.py new file mode 100644 index 00000000..52a622de --- /dev/null +++ b/images/chromium-headful/test_smooth_drag.py @@ -0,0 +1,194 @@ +#!/usr/bin/env python3 +""" +Demo: smooth Bezier drag_mouse vs linear drag_mouse. +Uploads a custom HTML page with a glowing cursor trail, +navigates the browser to it, records smooth then linear drags. +""" + +import json +import time +import urllib.request +import urllib.parse +import os + +BASE_URL = os.environ.get("BASE_URL", "https://mammary-unhorizontal-beula.ngrok-free.dev") +REC_ID = f"smooth-drag-demo-{int(time.time())}" +OUTPUT_FILE = "smooth_drag_demo.mp4" +HTML_PATH = "/tmp/cursor_demo.html" +HEADERS = {"Content-Type": "application/json", "ngrok-skip-browser-warning": "1"} + +BROWSER_CHROME_Y = 80 + +# Drag path through the target circles +DRAG_PATH = [ + [240, 240 + BROWSER_CHROME_Y], + [940, 190 + BROWSER_CHROME_Y], + [1690, 260 + BROWSER_CHROME_Y], + [1740, 740 + BROWSER_CHROME_Y], + [1000, 840 + BROWSER_CHROME_Y], + [220, 790 + BROWSER_CHROME_Y], + [540, 520 + BROWSER_CHROME_Y], + [1440, 520 + BROWSER_CHROME_Y], +] + +TARGET_IDS = ["t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7"] + + +def post(path, body=None): + data = json.dumps(body or {}).encode() + req = urllib.request.Request( + f"{BASE_URL}{path}", data=data, headers=HEADERS, method="POST" + ) + try: + with urllib.request.urlopen(req) as resp: + return resp.status, resp.read() + except urllib.error.HTTPError as e: + return e.code, e.read() + + +def get(path): + req = urllib.request.Request( + f"{BASE_URL}{path}", headers={"ngrok-skip-browser-warning": "1"}, method="GET" + ) + try: + with urllib.request.urlopen(req) as resp: + return resp.status, resp.read() + except urllib.error.HTTPError as e: + return e.code, e.read() + + +def write_file(remote_path, local_path): + with open(local_path, "rb") as f: + data = f.read() + encoded = urllib.parse.quote(remote_path) + req = urllib.request.Request( + f"{BASE_URL}/fs/write_file?path={encoded}", + data=data, + headers={"Content-Type": "application/octet-stream", "ngrok-skip-browser-warning": "1"}, + method="PUT", + ) + try: + with urllib.request.urlopen(req) as resp: + return resp.status, resp.read() + except urllib.error.HTTPError as e: + return e.code, e.read() + + +def drag(path, smooth, duration_ms=None, show=True): + body = {"path": path, "smooth": smooth} + if duration_ms is not None: + body["duration_ms"] = duration_ms + if show: + cmd_text = f"POST /computer/drag_mouse\n{json.dumps(body, indent=2)}" + run_js("kernel-cmd", cmd_text) + time.sleep(0.3) + status, resp = post("/computer/drag_mouse", body) + if status != 200: + print(f" WARNING: drag_mouse returned HTTP {status}: {resp.decode()}") + + +def move(x, y, smooth=False): + post("/computer/move_mouse", {"x": x, "y": y, "smooth": smooth}) + + +def navigate_to(url): + status, body = post("/playwright/execute", {"code": f"await page.goto('{url}', {{waitUntil: 'load'}});"}) + if status != 200: + print(f" WARNING: navigate HTTP {status}: {body.decode()}") + time.sleep(1.0) + + +def run_js(event, detail): + detail_json = json.dumps(detail) + code = f"await page.evaluate(() => {{ document.dispatchEvent(new CustomEvent('{event}', {{detail: {detail_json}}})); }});" + status, body = post("/playwright/execute", {"code": code}) + if status != 200: + print(f" WARNING: playwright/execute HTTP {status}: {body.decode()}") + + +# ── Upload HTML page ───────────────────────────────────────────────────────── +html_file = os.path.join(os.path.dirname(__file__), "cursor_demo.html") +print(f"Uploading {html_file} -> {HTML_PATH} ...") +status, body = write_file(HTML_PATH, html_file) +print(f" HTTP {status}: {body.decode() or '(empty)'}") +if status not in (200, 201): + print("Failed to upload HTML, aborting.") + exit(1) + +# ── Navigate to demo page ──────────────────────────────────────────────────── +print("Navigating to demo page...") +navigate_to(f"file://{HTML_PATH}") + +# ── Start recording ────────────────────────────────────────────────────────── +print("Starting recording...") +status, body = post("/recording/start", {"id": REC_ID, "framerate": 30}) +print(f" HTTP {status}: {body.decode() or '(empty)'}") +if status not in (200, 201): + print("Failed to start recording, aborting.") + exit(1) + +time.sleep(0.5) + +# ── Part 1: smooth Bezier drag ─────────────────────────────────────────────── +print("\n[SMOOTH] Bézier curve drag:") +run_js("kernel-mode", "smooth") +move(DRAG_PATH[0][0], DRAG_PATH[0][1], smooth=False) +time.sleep(0.5) + +print(f" Dragging through {len(DRAG_PATH)} waypoints (smooth=true, duration_ms=5000)") +drag(DRAG_PATH, smooth=True, duration_ms=5000) + +for tid in TARGET_IDS: + run_js("kernel-hit", {"id": tid, "mode": "smooth"}) + +time.sleep(1.5) + +# ── Part 2: linear drag ───────────────────────────────────────────────────── +print("\n[LINEAR] Linear interpolation drag:") +run_js("kernel-mode", "instant") +move(DRAG_PATH[0][0], DRAG_PATH[0][1], smooth=False) +time.sleep(0.5) + +print(f" Dragging through {len(DRAG_PATH)} waypoints (smooth=false, steps_per_segment=20, step_delay_ms=30)") +body = { + "path": DRAG_PATH, + "smooth": False, + "steps_per_segment": 20, + "step_delay_ms": 30, +} +cmd_text = f"POST /computer/drag_mouse\n{json.dumps(body, indent=2)}" +run_js("kernel-cmd", cmd_text) +time.sleep(0.3) +status, resp = post("/computer/drag_mouse", body) +if status != 200: + print(f" WARNING: drag_mouse returned HTTP {status}: {resp.decode()}") + +for tid in TARGET_IDS: + run_js("kernel-hit", {"id": tid, "mode": "instant"}) + +time.sleep(1.0) + +# ── Stop recording ─────────────────────────────────────────────────────────── +print("\nStopping recording...") +status, _ = post("/recording/stop", {"id": REC_ID}) +print(f" HTTP {status}") + +# ── Download ───────────────────────────────────────────────────────────────── +print(f"\nDownloading {OUTPUT_FILE}...") +for attempt in range(15): + status, data = get(f"/recording/download?id={REC_ID}") + if status == 202: + print(f" Still finalizing, retrying in 2s... (attempt {attempt + 1})") + time.sleep(2) + continue + if status == 200: + with open(OUTPUT_FILE, "wb") as f: + f.write(data) + size_kb = os.path.getsize(OUTPUT_FILE) / 1024 + print(f" Saved {OUTPUT_FILE} ({size_kb:.0f} KB)") + break + else: + print(f" HTTP {status}: {data.decode()}") + break + +print("\nDone.") diff --git a/server/api b/server/api index 778aa1cb11780c3fd7e65eaa26e9c14ca37af34d..8ffbdcaa75c6672f32134ec07882c374b4501e81 100755 GIT binary patch delta 6161970 zcma&P4_uU0_CJ2_GlPSoqJaS+&J0M1NN9*iqzwPUKbf^!R<6qogQ=OTt(F?vj6rEx z>pVTwt*pezjI4D6i&)zgv((mFr|j=qA3-$TY**ZBb5>n`?{lALa8UO3{rP&0&%NiK zd+xdSo_p@O=l z*Yb(6ZEJP#vupcHIK_qig*%68bvz*f^eE4g*6a052K^#z^(Mujo$IvpUUY z?RsVC75@4;GJm95NATBccPkTPTes@qWn*6QwTi3^aMWLQ^UV~oiDQk?hulm?x-u(UrNp{p-iX`{u$mjHo zBP_Ojp+-fH?i{Qa>V02+Wn7$DUKFGGBlG$L>V3<^ygB>X zXu(S!OVkGSjZF6!>}QeV7#sWY0e1c$k&OEBW}OUMo5SRfqHDFnzSfA*bq5$1?ZL@0 zqV419=B8DBf6a#-I^OrCrPt=B9NGKe!}-Tw%}4_JApAx@`59|$5cWC0-zS_?rabrm z_-}O7lmSl;8Z_h1Y4h@Kn3i|jeN%5Mym7kghMT9}FgI)QlHV;TUUd7)-`#!d($eX- zFLf;$yEyCG()$+W<=$Jg;DOAA_uc)#f}2ZSzso9JapR0J^Ot7N%$rwMal?X1#nUQA zYwkgLmi#j2tJ>2~s~_|ai~SnbY4`SP5`(`sTk6tSfU#js%dd=3X6&{yzx~EEwZo*m zcFc5tW2%*PZux4Y`klqmSYh&h`ltE4cElcD+iqg7=^2NrH-E%ykuPB1k*Xezda$tr zX<>P_gYiR*LWXLm;$0z5nr0;YZ1U^`TXQ!R2ir{6*Is8V_QWohN3gp9`!0h?cm?1! zKe1Y`mHF7%iE6uPRb$=1S#4XkBiNqk2);mJFu-b~kXF_BEX8w?W_1LgM%ac*us{mZ zJdIBxu7Xxau_Jga%c1Q{iZyq#$NOnVlHw5vq-f`o5-h|))t;eR;;?C!Rw^~NkG6PN zyg9(uU9GJjc5gR=$$CeIfvmbMj)t}rN6^anDaFiYx?|b;VGv96deG zNIw#mZn9{zQgY&mzB4U3&t~&}YO~e-i{e$LrK%-qt94cM?p$ij<$Tv7Q*pW0zc*2F)~cu zH~ZQ*x^bejOC@|h!L#k%;p*&Z-S}T-uk41;8oNe@?*jgjv0E$fjU8Hd|~`2y(Oy zH_eUprjZbUrA+3tdrj)jKl57QNF5ie4W0gLNs4Odnf_D?Fj4cN>h4VFa%NVS0<#CK z)zp-G^TP^d3M`=N|7wv8lPu-VxG%Z~vcuf8b4Cl72*g*_t=-5?r*D11EEA{^wL2$w zBXt;Iu+)@2`y@wyzdBK~&Kc5OPX3&g-8py8nIpqA4y?aDOv+qB@5?(p)vOCt@qDr~|M ztJxNrwQuhJs5|HOg-PAmhZcU_9WJ=fu6=gTsJ@}x?PARH{bIGGMYlmnFnpFTdRGRT za(_Ek(MQzcC7G7PH$WwtMmE(inaimR8pT@l?<98+2b-4lyN{_18D4&Ol4e^voH(So zs*N5OuT?JntUF`DGRd4ob}#$9J7d9plZi2zsa<^XRa~O>`h8_O7r)&1u0F1t?+-C{ zdPO&5TFS~LI-Xc*;LUnqv+OP(jmNI4`FirgRo!`-HmzFC^F!rbs4hSIU(2Mkt)}uX zj0&oDXopXlcr6(TJ<@d^n`S+j&bw>*wI)lcm9IM zwooros&?wJoKUzaZT+p`6;My)#EKVgkG5!akC${ab?WgqL*b_SC!UhE2#`7`@Xe)K z$nZAbYC`f+wX@Vr%g!4xNum~Rb){tu;LwCk9qPj-nPF~JY187T1}m0U=qm<`a;^9} zB4aj;j0dKd1RW+vkg4A&EIMHdGj4o8kQkWD3*GZ9l9d>|Y*#=wp01vjoZxHud)&cKZc z$DL->F1I*X8IGK53LY*-Ew|m+Vzrq*m#x!fX+gjFS!yW>TDO=BQ79ejd(9B_SH-;c z>lb<;Xs6z2=uWpI{nbm-xBp>s0XPacO%-`dp*DZ*X;)DT=`wJPb+inp(taFUreyjJScnS<4K#rx@~S7bGPY5{;_*>l9M zE3@*nK(kW<$k@t#N2gAiHojxm5fR>FglQ3R>YXv&@RXLx7H=kM(#Ex=EqV>fAllTD zByprI-J-V+wUp(LUuU3}el{~(wZlj7`OCbvM@zJ(tMAs!mgr<(U8zOwOo+WSeLK=c z>)DuC?Z%z{K}Nes(HOUf)e3*U0@LcOYmYif6RV{4`ilc9UCHC>03Y_~4zhA-Vcxf_4a?u&U(@4lEf<-PE{Ioi7S z)}^3gn4AZwYsf5jj8u1QmW^={#zr<}?^(%phHVjA)BC$+L2mSY)d#yRjE2GcL$u<( zfA3}>dtZ(WQ&%tEr!z*qxocmNgi{Z8>>DG)1W(*QmwM1oJ-Bv%p@dTp9^7Br9Zvi( zCk?$8K#!;{^jaPmjTq5W)Tkke-trIiN>lmUKGZ86CTjgP+h5L8r}>#JLT$%*{_U<% zr#TMP$s%dNcjAD~B6XVeBUlYkbiSfN(OT|bAB`iic4k!Md7-dKQBv8?@+9rczh+vz zm`<5@looYxOv*-t-Szk6RWp_=!y8M39T*l-`{C#zrMSP3R(^0ucb=+)3DfmFqo8yh zjqRqzShW7G@i+Z>EtLUjZmGwFN;odi`leN%P$}-*7!f2VQ(G1b-aiTW5>~2p92_&L ziaaUc!v%wel=$p(td?M&`cZjKslG<3Z!;a{1l^?rdAI5crT-xY&1B2y6RRx=IOD)g zU@la4DkvTYr;i}Mw=Pxe{5s<*iyl@*+b5&qHQOg<%foZQR6kw!!nzDI_~M;$+J8Heimodu=ZtWT3H zb3t-T+bFH-(+RmDOd~z$U~D}zGgXgA1hHQbE5pU5!EShQMAPX{BNR943Z1B^rGpu@ zcffUOZA&{X#V{?DGj?VXJY{4MR*^wd-zP7m-b4A8UvW|8%eu9ts@H-R;Tdsl*5^__ z1C>8owDq4SS&Y2e_RlA$v5_>DWUIA_(DyNLHl@LoWSQzwcoQtG22buen)QoU(>qyw zw7MCCL0@E)oTWtw2FYb`;a5!wTHi0TtyCq*b_>LItc^K>KVungGcmGAeQd;trrBQx zmCKN_3?wfhJztuZHS z>hqaH*0(?%a22aPj(H9H3qdJa7=T&dNJSPP#W(w#d$7RtP0$W}GmS=QfE0xFTL=&p z;#8WZe>;KG%n1W`u%`Xr=N8FH)>(72q8>Lr*mz9zZ)jUPpyAjs;E#>d7Pf6pt43aT?O62~+_n#m zO)Mlwzg=5ZaEdEIQ3TD79$tkY!uq6p-Q*eGqr-%~AmI92m>hppPS z?(o&xm)+qM&GdZ;KSRsv4gcb-_CX9@J#DzQygScGt^WIT zqddEIs2e^)>-s*&fTwHur!tLjlD7C%sJvm?#_n*kwy!&!rv2C*wrSQM#=;XYdZae% zht(ET+UI5iwZlJ*7z%AMLAn+($KQpgYv;JfBMTFM~0i8Vp-w?vW za0EdJ>%DnH!VsFn5o!owx_6}#hG6<Ys zQ%lBmW?JipL$?^M{R81-ID*%P;kY|9Q^Ik+*6I9-wI&a{3%V1HE@?GgLhA#C9cDSa@0_f8t6ZpFC%ZqtB<@8&szCuTc>-)$P$@Cs_Tw>4Kg_|uR? 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