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FA-85956 / Game economy crafting balance / Open access

Vendor sell saturation: Saturation is uncapped · case 01

Late sales collapse to the one-coin minimum instead of 40% value.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The saturation percentage is not capped at 60.

VERIFIED REPAIR

Restore `min(60, 5 * done)` at the saturation ceiling step.

Unsuccessful approach: A 50% cap overpays heavily saturated items.

Case contract

Selling qty units after `sales` units already sold today. Daily cap 20 units total; excess is returned. Per unit, with done = units sold today before it: saturation = min(60, 5*done) percent; unit = floor(base*(100-sat)/100), then floor(unit*(100+bonus)/100) with bonus neutral 0, friendly 5, honored 10; each unit pays at least 1.

Why this case matters

Game economies leak or destroy currency when one crafting or pricing rule is off by one boundary, rounding stage or state update; the defect is observable in exact integer outcomes.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(base_price, sales, qty, reputation):
    bonus = {'neutral': 0, 'friendly': 5, 'honored': 10}[reputation]
    gold = 0
    sold = 0
    for i in range(qty):
        done = sales + sold
        if done >= 20:
            break
        sat = 5 * done
        unit = base_price * (100 - sat) // 100
        unit = unit * (100 + bonus) // 100
        gold += max(1, unit)
        sold += 1
    return {'gold': gold, 'sold': sold, 'returned': qty - sold}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
  ('regression saturation ceiling #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('regression saturation ceiling #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
  ('regression saturation ceiling #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('regression saturation ceiling #2', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
  ('regression saturation ceiling #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression saturation ceiling #4', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression saturation ceiling #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
  ('regression saturation ceiling #3', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression saturation ceiling #4', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression saturation ceiling #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('regression saturation ceiling #3', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression saturation ceiling #4', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression saturation ceiling #2', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
  ('regression saturation ceiling #3', [70, 11, 3, 'friendly'], {'gold': 90, 'sold': 3, 'returned': 0}),
  ('regression saturation ceiling #4', [160, 15, 12, 'friendly'], {'gold': 335, 'sold': 5, 'returned': 7}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0})]]
for label, args, expected in cases[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
cap reached mid batch #1{'gold': 6, 'returned': 3, 'sold': 2}{'gold': 34, 'returned': 3, 'sold': 2}Failed
regression saturation ceiling #1{'gold': 331, 'returned': 0, 'sold': 7}{'gold': 532, 'returned': 0, 'sold': 7}Failed
regression saturation ceiling #2{'gold': 50, 'returned': 0, 'sold': 10}{'gold': 52, 'returned': 0, 'sold': 10}Failed
regression saturation ceiling #3{'gold': 9, 'returned': 0, 'sold': 6}{'gold': 12, 'returned': 0, 'sold': 6}Failed
regression saturation ceiling #4{'gold': 42, 'returned': 4, 'sold': 8}{'gold': 80, 'returned': 4, 'sold': 8}Failed
fresh day single sale #1{'gold': 9, 'returned': 0, 'sold': 1}{'gold': 9, 'returned': 0, 'sold': 1}Passed
cheap junk at saturation #1{'gold': 3, 'returned': 0, 'sold': 3}{'gold': 3, 'returned': 0, 'sold': 3}Passed
control #1{'gold': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed

SHA-256 / 25bc98ee1a1ed1a56f59598a732bd23a64e5cfbdc08d177937f58f596ba4d5ff

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(base_price, sales, qty, reputation):
    bonus = {'neutral': 0, 'friendly': 5, 'honored': 10}[reputation]
    gold = 0
    sold = 0
    for i in range(qty):
        done = sales + sold
        if done >= 20:
            break
        sat = min(50, 5 * done)
        unit = base_price * (100 - sat) // 100
        unit = unit * (100 + bonus) // 100
        gold += max(1, unit)
        sold += 1
    return {'gold': gold, 'sold': sold, 'returned': qty - sold}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
  ('regression saturation ceiling #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('regression saturation ceiling #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
  ('regression saturation ceiling #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('regression saturation ceiling #2', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
  ('regression saturation ceiling #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression saturation ceiling #4', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression saturation ceiling #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
  ('regression saturation ceiling #3', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression saturation ceiling #4', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression saturation ceiling #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('regression saturation ceiling #3', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression saturation ceiling #4', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression saturation ceiling #2', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
  ('regression saturation ceiling #3', [70, 11, 3, 'friendly'], {'gold': 90, 'sold': 3, 'returned': 0}),
  ('regression saturation ceiling #4', [160, 15, 12, 'friendly'], {'gold': 335, 'sold': 5, 'returned': 7}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0})]]
for label, args, expected in cases[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
cap reached mid batch #1{'gold': 44, 'returned': 3, 'sold': 2}{'gold': 34, 'returned': 3, 'sold': 2}Failed
regression saturation ceiling #1{'gold': 665, 'returned': 0, 'sold': 7}{'gold': 532, 'returned': 0, 'sold': 7}Failed
regression saturation ceiling #2{'gold': 56, 'returned': 0, 'sold': 10}{'gold': 52, 'returned': 0, 'sold': 10}Failed
regression saturation ceiling #3{'gold': 18, 'returned': 0, 'sold': 6}{'gold': 12, 'returned': 0, 'sold': 6}Failed
regression saturation ceiling #4{'gold': 96, 'returned': 4, 'sold': 8}{'gold': 80, 'returned': 4, 'sold': 8}Failed
fresh day single sale #1{'gold': 9, 'returned': 0, 'sold': 1}{'gold': 9, 'returned': 0, 'sold': 1}Passed
cheap junk at saturation #1{'gold': 3, 'returned': 0, 'sold': 3}{'gold': 3, 'returned': 0, 'sold': 3}Passed
control #1{'gold': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed

SHA-256 / 25cbd4af7214c54926478958c3d111717c2a1e426abd4c895f9c98764cc76233

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(base_price, sales, qty, reputation):
    bonus = {'neutral': 0, 'friendly': 5, 'honored': 10}[reputation]
    gold = 0
    sold = 0
    for i in range(qty):
        done = sales + sold
        if done >= 20:
            break
        sat = min(60, 5 * done)
        unit = base_price * (100 - sat) // 100
        unit = unit * (100 + bonus) // 100
        gold += max(1, unit)
        sold += 1
    return {'gold': gold, 'sold': sold, 'returned': qty - sold}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
  ('regression saturation ceiling #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('regression saturation ceiling #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
  ('regression saturation ceiling #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('regression saturation ceiling #2', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
  ('regression saturation ceiling #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression saturation ceiling #4', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression saturation ceiling #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
  ('regression saturation ceiling #3', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression saturation ceiling #4', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression saturation ceiling #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('regression saturation ceiling #3', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression saturation ceiling #4', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression saturation ceiling #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression saturation ceiling #2', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
  ('regression saturation ceiling #3', [70, 11, 3, 'friendly'], {'gold': 90, 'sold': 3, 'returned': 0}),
  ('regression saturation ceiling #4', [160, 15, 12, 'friendly'], {'gold': 335, 'sold': 5, 'returned': 7}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0})]]
for label, args, expected in cases[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
cap reached mid batch #1{'gold': 34, 'returned': 3, 'sold': 2}{'gold': 34, 'returned': 3, 'sold': 2}Passed
regression saturation ceiling #1{'gold': 532, 'returned': 0, 'sold': 7}{'gold': 532, 'returned': 0, 'sold': 7}Passed
regression saturation ceiling #2{'gold': 52, 'returned': 0, 'sold': 10}{'gold': 52, 'returned': 0, 'sold': 10}Passed
regression saturation ceiling #3{'gold': 12, 'returned': 0, 'sold': 6}{'gold': 12, 'returned': 0, 'sold': 6}Passed
regression saturation ceiling #4{'gold': 80, 'returned': 4, 'sold': 8}{'gold': 80, 'returned': 4, 'sold': 8}Passed
fresh day single sale #1{'gold': 9, 'returned': 0, 'sold': 1}{'gold': 9, 'returned': 0, 'sold': 1}Passed
cheap junk at saturation #1{'gold': 3, 'returned': 0, 'sold': 3}{'gold': 3, 'returned': 0, 'sold': 3}Passed
control #1{'gold': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed

SHA-256 / 3de6f2650b2ed52739957ed3c10c157a373fd25ac18f2b031b17a8f6145d751c

Verification & scope

Deterministic toy contract stipulated for this model; integer or exact arithmetic only, not a reproduction of any specific game engine. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:50:45.077409+00:00.

Case digest / 6b4a59b93da85e02d7cac691cbcdff68e130178d12d6204bb71450aedece5ec4