Problem:
Score : 200 points

Problem Statement

Takahashi has a deposit of 100 yen (the currency of Japan) in AtCoder Bank.

The bank pays an annual interest rate of 1 % compounded annually. (A fraction of less than one yen is discarded.)

Assuming that nothing other than the interest affects Takahashi's balance, in how many years does the balance reach X yen or above for the first time?

Constraints

101 \le X \le 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the number of years it takes for Takahashi's balance to reach X yen or above for the first time.

Sample Input 1

103

Sample Output 1

3

The balance after one year is 101 yen.

The balance after two years is 102 yen.

The balance after three years is 103 yen.

Thus, it takes three years for the balance to reach 103 yen or above.

Sample Input 2

1000000000000000000

Sample Output 2

3760

Sample Input 3

1333333333

Sample Output 3

1706

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

"use strict";
var bigInt = function (undefined) { "use strict"; var BASE = 1e7, LOG_BASE = 7, MAX_INT = 9007199254740992, MAX_INT_ARR = smallToArray(MAX_INT), LOG_MAX_INT = Math.log(MAX_INT); function Integer(v, radix) { if (typeof v === "undefined") return Integer[0]; if (typeof radix !== "undefined") return +radix === 10 ? parseValue(v) : parseBase(v, radix); return parseValue(v) } function BigInteger(value, sign) { this.value = value; this.sign = sign; this.isSmall = false } BigInteger.prototype = Object.create(Integer.prototype); function SmallInteger(value) { this.value = value; this.sign = value < 0; this.isSmall = true } SmallInteger.prototype = Object.create(Integer.prototype); function isPrecise(n) { return -MAX_INT < n && n < MAX_INT } function smallToArray(n) { if (n < 1e7) return [n]; if (n < 1e14) return [n % 1e7, Math.floor(n / 1e7)]; return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)] } function arrayToSmall(arr) { trim(arr); var length = arr.length; if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) { switch (length) { case 0: return 0; case 1: return arr[0]; case 2: return arr[0] + arr[1] * BASE; default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE } } return arr } function trim(v) { var i = v.length; while (v[--i] === 0); v.length = i + 1 } function createArray(length) { var x = new Array(length); var i = -1; while (++i < length) { x[i] = 0 } return x } function truncate(n) { if (n > 0) return Math.floor(n); return Math.ceil(n) } function add(a, b) { var l_a = a.length, l_b = b.length, r = new Array(l_a), carry = 0, base = BASE, sum, i; for (i = 0; i < l_b; i++) { sum = a[i] + b[i] + carry; carry = sum >= base ? 1 : 0; r[i] = sum - carry * base } while (i < l_a) { sum = a[i] + carry; carry = sum === base ? 1 : 0; r[i++] = sum - carry * base } if (carry > 0) r.push(carry); return r } function addAny(a, b) { if (a.length >= b.length) return add(a, b); return add(b, a) } function addSmall(a, carry) { var l = a.length, r = new Array(l), base = BASE, sum, i; for (i = 0; i < l; i++) { sum = a[i] - base + carry; carry = Math.floor(sum / base); r[i] = sum - carry * base; carry += 1 } while (carry > 0) { r[i++] = carry % base; carry = Math.floor(carry / base) } return r } BigInteger.prototype.add = function (v) { var n = parseValue(v); if (this.sign !== n.sign) { return this.subtract(n.negate()) } var a = this.value, b = n.value; if (n.isSmall) { return new BigInteger(addSmall(a, Math.abs(b)), this.sign) } return new BigInteger(addAny(a, b), this.sign) }; BigInteger.prototype.plus = BigInteger.prototype.add; SmallInteger.prototype.add = function (v) { var n = parseValue(v); var a = this.value; if (a < 0 !== n.sign) { return this.subtract(n.negate()) } var b = n.value; if (n.isSmall) { if (isPrecise(a + b)) return new SmallInteger(a + b); b = smallToArray(Math.abs(b)) } return new BigInteger(addSmall(b, Math.abs(a)), a < 0) }; SmallInteger.prototype.plus = SmallInteger.prototype.add; function subtract(a, b) { var a_l = a.length, b_l = b.length, r = new Array(a_l), borrow = 0, base = BASE, i, difference; for (i = 0; i < b_l; i++) { difference = a[i] - borrow - b[i]; if (difference < 0) { difference += base; borrow = 1 } else borrow = 0; r[i] = difference } for (i = b_l; i < a_l; i++) { difference = a[i] - borrow; if (difference < 0) difference += base; else { r[i++] = difference; break } r[i] = difference } for (; i < a_l; i++) { r[i] = a[i] } trim(r); return r } function subtractAny(a, b, sign) { var value; if (compareAbs(a, b) >= 0) { value = subtract(a, b) } else { value = subtract(b, a); sign = !sign } value = arrayToSmall(value); if (typeof value === "number") { if (sign) value = -value; return new SmallInteger(value) } return new BigInteger(value, sign) } function subtractSmall(a, b, sign) { var l = a.length, r = new Array(l), carry = -b, base = BASE, i, difference; for (i = 0; i < l; i++) { difference = a[i] + carry; carry = Math.floor(difference / base); difference %= base; r[i] = difference < 0 ? difference + base : difference } r = arrayToSmall(r); if (typeof r === "number") { if (sign) r = -r; return new SmallInteger(r) } return new BigInteger(r, sign) } BigInteger.prototype.subtract = function (v) { var n = parseValue(v); if (this.sign !== n.sign) { return this.add(n.negate()) } var a = this.value, b = n.value; if (n.isSmall) return subtractSmall(a, Math.abs(b), this.sign); return subtractAny(a, b, this.sign) }; BigInteger.prototype.minus = BigInteger.prototype.subtract; SmallInteger.prototype.subtract = function (v) { var n = parseValue(v); var a = this.value; if (a < 0 !== n.sign) { return this.add(n.negate()) } var b = n.value; if (n.isSmall) { return new SmallInteger(a - b) } return subtractSmall(b, Math.abs(a), a >= 0) }; SmallInteger.prototype.minus = SmallInteger.prototype.subtract; BigInteger.prototype.negate = function () { return new BigInteger(this.value, !this.sign) }; SmallInteger.prototype.negate = function () { var sign = this.sign; var small = new SmallInteger(-this.value); small.sign = !sign; return small }; BigInteger.prototype.abs = function () { return new BigInteger(this.value, false) }; SmallInteger.prototype.abs = function () { return new SmallInteger(Math.abs(this.value)) }; function multiplyLong(a, b) { var a_l = a.length, b_l = b.length, l = a_l + b_l, r = createArray(l), base = BASE, product, carry, i, a_i, b_j; for (i = 0; i < a_l; ++i) { a_i = a[i]; for (var j = 0; j < b_l; ++j) { b_j = b[j]; product = a_i * b_j + r[i + j]; carry = Math.floor(product / base); r[i + j] = product - carry * base; r[i + j + 1] += carry } } trim(r); return r } function multiplySmall(a, b) { var l = a.length, r = new Array(l), base = BASE, carry = 0, product, i; for (i = 0; i < l; i++) { product = a[i] * b + carry; carry = Math.floor(product / base); r[i] = product - carry * base } while (carry > 0) { r[i++] = carry % base; carry = Math.floor(carry / base) } return r } function shiftLeft(x, n) { var r = []; while (n-- > 0) r.push(0); return r.concat(x) } function multiplyKaratsuba(x, y) { var n = Math.max(x.length, y.length); if (n <= 30) return multiplyLong(x, y); n = Math.ceil(n / 2); var b = x.slice(n), a = x.slice(0, n), d = y.slice(n), c = y.slice(0, n); var ac = multiplyKaratsuba(a, c), bd = multiplyKaratsuba(b, d), abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d)); var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n)); trim(product); return product } function useKaratsuba(l1, l2) { return -.012 * l1 - .012 * l2 + 15e-6 * l1 * l2 > 0 } BigInteger.prototype.multiply = function (v) { var n = parseValue(v), a = this.value, b = n.value, sign = this.sign !== n.sign, abs; if (n.isSmall) { if (b === 0) return Integer[0]; if (b === 1) return this; if (b === -1) return this.negate(); abs = Math.abs(b); if (abs < BASE) { return new BigInteger(multiplySmall(a, abs), sign) } b = smallToArray(abs) } if (useKaratsuba(a.length, b.length)) return new BigInteger(multiplyKaratsuba(a, b), sign); return new BigInteger(multiplyLong(a, b), sign) }; BigInteger.prototype.times = BigInteger.prototype.multiply; function multiplySmallAndArray(a, b, sign) { if (a < BASE) { return new BigInteger(multiplySmall(b, a), sign) } return new BigInteger(multiplyLong(b, smallToArray(a)), sign) } SmallInteger.prototype._multiplyBySmall = function (a) { if (isPrecise(a.value * this.value)) { return new SmallInteger(a.value * this.value) } return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign) }; BigInteger.prototype._multiplyBySmall = function (a) { if (a.value === 0) return Integer[0]; if (a.value === 1) return this; if (a.value === -1) return this.negate(); return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign) }; SmallInteger.prototype.multiply = function (v) { return parseValue(v)._multiplyBySmall(this) }; SmallInteger.prototype.times = SmallInteger.prototype.multiply; function square(a) { var l = a.length, r = createArray(l + l), base = BASE, product, carry, i, a_i, a_j; for (i = 0; i < l; i++) { a_i = a[i]; carry = 0 - a_i * a_i; for (var j = i; j < l; j++) { a_j = a[j]; product = 2 * (a_i * a_j) + r[i + j] + carry; carry = Math.floor(product / base); r[i + j] = product - carry * base } r[i + l] = carry } trim(r); return r } BigInteger.prototype.square = function () { return new BigInteger(square(this.value), false) }; SmallInteger.prototype.square = function () { var value = this.value * this.value; if (isPrecise(value)) return new SmallInteger(value); return new BigInteger(square(smallToArray(Math.abs(this.value))), false) }; function divMod1(a, b) { var a_l = a.length, b_l = b.length, base = BASE, result = createArray(b.length), divisorMostSignificantDigit = b[b_l - 1], lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)), remainder = multiplySmall(a, lambda), divisor = multiplySmall(b, lambda), quotientDigit, shift, carry, borrow, i, l, q; if (remainder.length <= a_l) remainder.push(0); divisor.push(0); divisorMostSignificantDigit = divisor[b_l - 1]; for (shift = a_l - b_l; shift >= 0; shift--) { quotientDigit = base - 1; if (remainder[shift + b_l] !== divisorMostSignificantDigit) { quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit) } carry = 0; borrow = 0; l = divisor.length; for (i = 0; i < l; i++) { carry += quotientDigit * divisor[i]; q = Math.floor(carry / base); borrow += remainder[shift + i] - (carry - q * base); carry = q; if (borrow < 0) { remainder[shift + i] = borrow + base; borrow = -1 } else { remainder[shift + i] = borrow; borrow = 0 } } while (borrow !== 0) { quotientDigit -= 1; carry = 0; for (i = 0; i < l; i++) { carry += remainder[shift + i] - base + divisor[i]; if (carry < 0) { remainder[shift + i] = carry + base; carry = 0 } else { remainder[shift + i] = carry; carry = 1 } } borrow += carry } result[shift] = quotientDigit } remainder = divModSmall(remainder, lambda)[0]; return [arrayToSmall(result), arrayToSmall(remainder)] } function divMod2(a, b) { var a_l = a.length, b_l = b.length, result = [], part = [], base = BASE, guess, xlen, highx, highy, check; while (a_l) { part.unshift(a[--a_l]); trim(part); if (compareAbs(part, b) < 0) { result.push(0); continue } xlen = part.length; highx = part[xlen - 1] * base + part[xlen - 2]; highy = b[b_l - 1] * base + b[b_l - 2]; if (xlen > b_l) { highx = (highx + 1) * base } guess = Math.ceil(highx / highy); do { check = multiplySmall(b, guess); if (compareAbs(check, part) <= 0) break; guess-- } while (guess); result.push(guess); part = subtract(part, check) } result.reverse(); return [arrayToSmall(result), arrayToSmall(part)] } function divModSmall(value, lambda) { var length = value.length, quotient = createArray(length), base = BASE, i, q, remainder, divisor; remainder = 0; for (i = length - 1; i >= 0; --i) { divisor = remainder * base + value[i]; q = truncate(divisor / lambda); remainder = divisor - q * lambda; quotient[i] = q | 0 } return [quotient, remainder | 0] } function divModAny(self, v) { var value, n = parseValue(v); var a = self.value, b = n.value; var quotient; if (b === 0) throw new Error("Cannot divide by zero"); if (self.isSmall) { if (n.isSmall) { return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)] } return [Integer[0], self] } if (n.isSmall) { if (b === 1) return [self, Integer[0]]; if (b == -1) return [self.negate(), Integer[0]]; var abs = Math.abs(b); if (abs < BASE) { value = divModSmall(a, abs); quotient = arrayToSmall(value[0]); var remainder = value[1]; if (self.sign) remainder = -remainder; if (typeof quotient === "number") { if (self.sign !== n.sign) quotient = -quotient; return [new SmallInteger(quotient), new SmallInteger(remainder)] } return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)] } b = smallToArray(abs) } var comparison = compareAbs(a, b); if (comparison === -1) return [Integer[0], self]; if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]]; if (a.length + b.length <= 200) value = divMod1(a, b); else value = divMod2(a, b); quotient = value[0]; var qSign = self.sign !== n.sign, mod = value[1], mSign = self.sign; if (typeof quotient === "number") { if (qSign) quotient = -quotient; quotient = new SmallInteger(quotient) } else quotient = new BigInteger(quotient, qSign); if (typeof mod === "number") { if (mSign) mod = -mod; mod = new SmallInteger(mod) } else mod = new BigInteger(mod, mSign); return [quotient, mod] } BigInteger.prototype.divmod = function (v) { var result = divModAny(this, v); return { quotient: result[0], remainder: result[1] } }; SmallInteger.prototype.divmod = BigInteger.prototype.divmod; BigInteger.prototype.divide = function (v) { return divModAny(this, v)[0] }; SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide; BigInteger.prototype.mod = function (v) { return divModAny(this, v)[1] }; SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod; BigInteger.prototype.pow = function (v) { var n = parseValue(v), a = this.value, b = n.value, value, x, y; if (b === 0) return Integer[1]; if (a === 0) return Integer[0]; if (a === 1) return Integer[1]; if (a === -1) return n.isEven() ? Integer[1] : Integer[-1]; if (n.sign) { return Integer[0] } if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large."); if (this.isSmall) { if (isPrecise(value = Math.pow(a, b))) return new SmallInteger(truncate(value)) } x = this; y = Integer[1]; while (true) { if (b & 1 === 1) { y = y.times(x); --b } if (b === 0) break; b /= 2; x = x.square() } return y }; SmallInteger.prototype.pow = BigInteger.prototype.pow; BigInteger.prototype.modPow = function (exp, mod) { exp = parseValue(exp); mod = parseValue(mod); if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0"); var r = Integer[1], base = this.mod(mod); while (exp.isPositive()) { if (base.isZero()) return Integer[0]; if (exp.isOdd()) r = r.multiply(base).mod(mod); exp = exp.divide(2); base = base.square().mod(mod) } return r }; SmallInteger.prototype.modPow = BigInteger.prototype.modPow; function compareAbs(a, b) { if (a.length !== b.length) { return a.length > b.length ? 1 : -1 } for (var i = a.length - 1; i >= 0; i--) { if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1 } return 0 } BigInteger.prototype.compareAbs = function (v) { var n = parseValue(v), a = this.value, b = n.value; if (n.isSmall) return 1; return compareAbs(a, b) }; SmallInteger.prototype.compareAbs = function (v) { var n = parseValue(v), a = Math.abs(this.value), b = n.value; if (n.isSmall) { b = Math.abs(b); return a === b ? 0 : a > b ? 1 : -1 } return -1 }; BigInteger.prototype.compare = function (v) { if (v === Infinity) { return -1 } if (v === -Infinity) { return 1 } var n = parseValue(v), a = this.value, b = n.value; if (this.sign !== n.sign) { return n.sign ? 1 : -1 } if (n.isSmall) { return this.sign ? -1 : 1 } return compareAbs(a, b) * (this.sign ? -1 : 1) }; BigInteger.prototype.compareTo = BigInteger.prototype.compare; SmallInteger.prototype.compare = function (v) { if (v === Infinity) { return -1 } if (v === -Infinity) { return 1 } var n = parseValue(v), a = this.value, b = n.value; if (n.isSmall) { return a == b ? 0 : a > b ? 1 : -1 } if (a < 0 !== n.sign) { return a < 0 ? -1 : 1 } return a < 0 ? 1 : -1 }; SmallInteger.prototype.compareTo = SmallInteger.prototype.compare; BigInteger.prototype.equals = function (v) { return this.compare(v) === 0 }; SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals; BigInteger.prototype.notEquals = function (v) { return this.compare(v) !== 0 }; SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals; BigInteger.prototype.greater = function (v) { return this.compare(v) > 0 }; SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater; BigInteger.prototype.lesser = function (v) { return this.compare(v) < 0 }; SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser; BigInteger.prototype.greaterOrEquals = function (v) { return this.compare(v) >= 0 }; SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals; BigInteger.prototype.lesserOrEquals = function (v) { return this.compare(v) <= 0 }; SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals; BigInteger.prototype.isEven = function () { return (this.value[0] & 1) === 0 }; SmallInteger.prototype.isEven = function () { return (this.value & 1) === 0 }; BigInteger.prototype.isOdd = function () { return (this.value[0] & 1) === 1 }; SmallInteger.prototype.isOdd = function () { return (this.value & 1) === 1 }; BigInteger.prototype.isPositive = function () { return !this.sign }; SmallInteger.prototype.isPositive = function () { return this.value > 0 }; BigInteger.prototype.isNegative = function () { return this.sign }; SmallInteger.prototype.isNegative = function () { return this.value < 0 }; BigInteger.prototype.isUnit = function () { return false }; SmallInteger.prototype.isUnit = function () { return Math.abs(this.value) === 1 }; BigInteger.prototype.isZero = function () { return false }; SmallInteger.prototype.isZero = function () { return this.value === 0 }; BigInteger.prototype.isDivisibleBy = function (v) { var n = parseValue(v); var value = n.value; if (value === 0) return false; if (value === 1) return true; if (value === 2) return this.isEven(); return this.mod(n).equals(Integer[0]) }; SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy; function isBasicPrime(v) { var n = v.abs(); if (n.isUnit()) return false; if (n.equals(2) || n.equals(3) || n.equals(5)) return true; if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false; if (n.lesser(25)) return true } BigInteger.prototype.isPrime = function () { var isPrime = isBasicPrime(this); if (isPrime !== undefined) return isPrime; var n = this.abs(), nPrev = n.prev(); var a = [2, 3, 5, 7, 11, 13, 17, 19], b = nPrev, d, t, i, x; while (b.isEven()) b = b.divide(2); for (i = 0; i < a.length; i++) { x = bigInt(a[i]).modPow(b, n); if (x.equals(Integer[1]) || x.equals(nPrev)) continue; for (t = true, d = b; t && d.lesser(nPrev); d = d.multiply(2)) { x = x.square().mod(n); if (x.equals(nPrev)) t = false } if (t) return false } return true }; SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime; BigInteger.prototype.isProbablePrime = function (iterations) { var isPrime = isBasicPrime(this); if (isPrime !== undefined) return isPrime; var n = this.abs(); var t = iterations === undefined ? 5 : iterations; for (var i = 0; i < t; i++) { var a = bigInt.randBetween(2, n.minus(2)); if (!a.modPow(n.prev(), n).isUnit()) return false } return true }; SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime; BigInteger.prototype.modInv = function (n) { var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR; while (!newR.equals(bigInt.zero)) { q = r.divide(newR); lastT = t; lastR = r; t = newT; r = newR; newT = lastT.subtract(q.multiply(newT)); newR = lastR.subtract(q.multiply(newR)) } if (!r.equals(1)) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime"); if (t.compare(0) === -1) { t = t.add(n) } if (this.isNegative()) { return t.negate() } return t }; SmallInteger.prototype.modInv = BigInteger.prototype.modInv; BigInteger.prototype.next = function () { var value = this.value; if (this.sign) { return subtractSmall(value, 1, this.sign) } return new BigInteger(addSmall(value, 1), this.sign) }; SmallInteger.prototype.next = function () { var value = this.value; if (value + 1 < MAX_INT) return new SmallInteger(value + 1); return new BigInteger(MAX_INT_ARR, false) }; BigInteger.prototype.prev = function () { var value = this.value; if (this.sign) { return new BigInteger(addSmall(value, 1), true) } return subtractSmall(value, 1, this.sign) }; SmallInteger.prototype.prev = function () { var value = this.value; if (value - 1 > -MAX_INT) return new SmallInteger(value - 1); return new BigInteger(MAX_INT_ARR, true) }; var powersOfTwo = [1]; while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]); var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1]; function shift_isSmall(n) { return (typeof n === "number" || typeof n === "string") && +Math.abs(n) <= BASE || n instanceof BigInteger && n.value.length <= 1 } BigInteger.prototype.shiftLeft = function (n) { if (!shift_isSmall(n)) { throw new Error(String(n) + " is too large for shifting.") } n = +n; if (n < 0) return this.shiftRight(-n); var result = this; if (result.isZero()) return result; while (n >= powers2Length) { result = result.multiply(highestPower2); n -= powers2Length - 1 } return result.multiply(powersOfTwo[n]) }; SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft; BigInteger.prototype.shiftRight = function (n) { var remQuo; if (!shift_isSmall(n)) { throw new Error(String(n) + " is too large for shifting.") } n = +n; if (n < 0) return this.shiftLeft(-n); var result = this; while (n >= powers2Length) { if (result.isZero() || result.isNegative() && result.isUnit()) return result; remQuo = divModAny(result, highestPower2); result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; n -= powers2Length - 1 } remQuo = divModAny(result, powersOfTwo[n]); return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0] }; SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight; function bitwise(x, y, fn) { y = parseValue(y); var xSign = x.isNegative(), ySign = y.isNegative(); var xRem = xSign ? x.not() : x, yRem = ySign ? y.not() : y; var xDigit = 0, yDigit = 0; var xDivMod = null, yDivMod = null; var result = []; while (!xRem.isZero() || !yRem.isZero()) { xDivMod = divModAny(xRem, highestPower2); xDigit = xDivMod[1].toJSNumber(); if (xSign) { xDigit = highestPower2 - 1 - xDigit } yDivMod = divModAny(yRem, highestPower2); yDigit = yDivMod[1].toJSNumber(); if (ySign) { yDigit = highestPower2 - 1 - yDigit } xRem = xDivMod[0]; yRem = yDivMod[0]; result.push(fn(xDigit, yDigit)) } var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0); for (var i = result.length - 1; i >= 0; i -= 1) { sum = sum.multiply(highestPower2).add(bigInt(result[i])) } return sum } BigInteger.prototype.not = function () { return this.negate().prev() }; SmallInteger.prototype.not = BigInteger.prototype.not; BigInteger.prototype.and = function (n) { return bitwise(this, n, function (a, b) { return a & b }) }; SmallInteger.prototype.and = BigInteger.prototype.and; BigInteger.prototype.or = function (n) { return bitwise(this, n, function (a, b) { return a | b }) }; SmallInteger.prototype.or = BigInteger.prototype.or; BigInteger.prototype.xor = function (n) { return bitwise(this, n, function (a, b) { return a ^ b }) }; SmallInteger.prototype.xor = BigInteger.prototype.xor; var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I; function roughLOB(n) { var v = n.value, x = typeof v === "number" ? v | LOBMASK_I : v[0] + v[1] * BASE | LOBMASK_BI; return x & -x } function integerLogarithm(value, base) { if (base.compareTo(value) <= 0) { var tmp = integerLogarithm(value, base.square(base)); var p = tmp.p; var e = tmp.e; var t = p.multiply(base); return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 } } return { p: bigInt(1), e: 0 } } BigInteger.prototype.bitLength = function () { var n = this; if (n.compareTo(bigInt(0)) < 0) { n = n.negate().subtract(bigInt(1)) } if (n.compareTo(bigInt(0)) === 0) { return bigInt(0) } return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1)) }; SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength; function max(a, b) { a = parseValue(a); b = parseValue(b); return a.greater(b) ? a : b } function min(a, b) { a = parseValue(a); b = parseValue(b); return a.lesser(b) ? a : b } function gcd(a, b) { a = parseValue(a).abs(); b = parseValue(b).abs(); if (a.equals(b)) return a; if (a.isZero()) return b; if (b.isZero()) return a; var c = Integer[1], d, t; while (a.isEven() && b.isEven()) { d = Math.min(roughLOB(a), roughLOB(b)); a = a.divide(d); b = b.divide(d); c = c.multiply(d) } while (a.isEven()) { a = a.divide(roughLOB(a)) } do { while (b.isEven()) { b = b.divide(roughLOB(b)) } if (a.greater(b)) { t = b; b = a; a = t } b = b.subtract(a) } while (!b.isZero()); return c.isUnit() ? a : a.multiply(c) } function lcm(a, b) { a = parseValue(a).abs(); b = parseValue(b).abs(); return a.divide(gcd(a, b)).multiply(b) } function randBetween(a, b) { a = parseValue(a); b = parseValue(b); var low = min(a, b), high = max(a, b); var range = high.subtract(low).add(1); if (range.isSmall) return low.add(Math.floor(Math.random() * range)); var length = range.value.length - 1; var result = [], restricted = true; for (var i = length; i >= 0; i--) { var top = restricted ? range.value[i] : BASE; var digit = truncate(Math.random() * top); result.unshift(digit); if (digit < top) restricted = false } result = arrayToSmall(result); return low.add(typeof result === "number" ? new SmallInteger(result) : new BigInteger(result, false)) } var parseBase = function (text, base) { var length = text.length; var i; var absBase = Math.abs(base); for (var i = 0; i < length; i++) { var c = text[i].toLowerCase(); if (c === "-") continue; if (/[a-z0-9]/.test(c)) { if (/[0-9]/.test(c) && +c >= absBase) { if (c === "1" && absBase === 1) continue; throw new Error(c + " is not a valid digit in base " + base + ".") } else if (c.charCodeAt(0) - 87 >= absBase) { throw new Error(c + " is not a valid digit in base " + base + ".") } } } if (2 <= base && base <= 36) { if (length <= LOG_MAX_INT / Math.log(base)) { var result = parseInt(text, base); if (isNaN(result)) { throw new Error(c + " is not a valid digit in base " + base + ".") } return new SmallInteger(parseInt(text, base)) } } base = parseValue(base); var digits = []; var isNegative = text[0] === "-"; for (i = isNegative ? 1 : 0; i < text.length; i++) { var c = text[i].toLowerCase(), charCode = c.charCodeAt(0); if (48 <= charCode && charCode <= 57) digits.push(parseValue(c)); else if (97 <= charCode && charCode <= 122) digits.push(parseValue(c.charCodeAt(0) - 87)); else if (c === "<") { var start = i; do { i++ } while (text[i] !== ">"); digits.push(parseValue(text.slice(start + 1, i))) } else throw new Error(c + " is not a valid character") } return parseBaseFromArray(digits, base, isNegative) }; function parseBaseFromArray(digits, base, isNegative) { var val = Integer[0], pow = Integer[1], i; for (i = digits.length - 1; i >= 0; i--) { val = val.add(digits[i].times(pow)); pow = pow.times(base) } return isNegative ? val.negate() : val } function stringify(digit) { if (digit <= 35) { return "0123456789abcdefghijklmnopqrstuvwxyz".charAt(digit) } return "<" + digit + ">" } function toBase(n, base) { base = bigInt(base); if (base.isZero()) { if (n.isZero()) return { value: [0], isNegative: false }; throw new Error("Cannot convert nonzero numbers to base 0.") } if (base.equals(-1)) { if (n.isZero()) return { value: [0], isNegative: false }; if (n.isNegative()) return { value: [].concat.apply([], Array.apply(null, Array(-n)).map(Array.prototype.valueOf, [1, 0])), isNegative: false }; var arr = Array.apply(null, Array(+n - 1)).map(Array.prototype.valueOf, [0, 1]); arr.unshift([1]); return { value: [].concat.apply([], arr), isNegative: false } } var neg = false; if (n.isNegative() && base.isPositive()) { neg = true; n = n.abs() } if (base.equals(1)) { if (n.isZero()) return { value: [0], isNegative: false }; return { value: Array.apply(null, Array(+n)).map(Number.prototype.valueOf, 1), isNegative: neg } } var out = []; var left = n, divmod; while (left.isNegative() || left.compareAbs(base) >= 0) { divmod = left.divmod(base); left = divmod.quotient; var digit = divmod.remainder; if (digit.isNegative()) { digit = base.minus(digit).abs(); left = left.next() } out.push(digit.toJSNumber()) } out.push(left.toJSNumber()); return { value: out.reverse(), isNegative: neg } } function toBaseString(n, base) { var arr = toBase(n, base); return (arr.isNegative ? "-" : "") + arr.value.map(stringify).join("") } BigInteger.prototype.toArray = function (radix) { return toBase(this, radix) }; SmallInteger.prototype.toArray = function (radix) { return toBase(this, radix) }; BigInteger.prototype.toString = function (radix) { if (radix === undefined) radix = 10; if (radix !== 10) return toBaseString(this, radix); var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit; while (--l >= 0) { digit = String(v[l]); str += zeros.slice(digit.length) + digit } var sign = this.sign ? "-" : ""; return sign + str }; SmallInteger.prototype.toString = function (radix) { if (radix === undefined) radix = 10; if (radix != 10) return toBaseString(this, radix); return String(this.value) }; BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString() }; BigInteger.prototype.valueOf = function () { return parseInt(this.toString(), 10) }; BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf; SmallInteger.prototype.valueOf = function () { return this.value }; SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf; function parseStringValue(v) { if (isPrecise(+v)) { var x = +v; if (x === truncate(x)) return new SmallInteger(x); throw new Error("Invalid integer: " + v) } var sign = v[0] === "-"; if (sign) v = v.slice(1); var split = v.split(/e/i); if (split.length > 2) throw new Error("Invalid integer: " + split.join("e")); if (split.length === 2) { var exp = split[1]; if (exp[0] === "+") exp = exp.slice(1); exp = +exp; if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent."); var text = split[0]; var decimalPlace = text.indexOf("."); if (decimalPlace >= 0) { exp -= text.length - decimalPlace - 1; text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1) } if (exp < 0) throw new Error("Cannot include negative exponent part for integers"); text += new Array(exp + 1).join("0"); v = text } var isValid = /^([0-9][0-9]*)$/.test(v); if (!isValid) throw new Error("Invalid integer: " + v); var r = [], max = v.length, l = LOG_BASE, min = max - l; while (max > 0) { r.push(+v.slice(min, max)); min -= l; if (min < 0) min = 0; max -= l } trim(r); return new BigInteger(r, sign) } function parseNumberValue(v) { if (isPrecise(v)) { if (v !== truncate(v)) throw new Error(v + " is not an integer."); return new SmallInteger(v) } return parseStringValue(v.toString()) } function parseValue(v) { if (typeof v === "number") { return parseNumberValue(v) } if (typeof v === "string") { return parseStringValue(v) } return v } for (var i = 0; i < 1e3; i++) { Integer[i] = new SmallInteger(i); if (i > 0) Integer[-i] = new SmallInteger(-i) } Integer.one = Integer[1]; Integer.zero = Integer[0]; Integer.minusOne = Integer[-1]; Integer.max = max; Integer.min = min; Integer.gcd = gcd; Integer.lcm = lcm; Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger }; Integer.randBetween = randBetween; Integer.fromArray = function (digits, base, isNegative) { return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative) }; return Integer }();
"use strict";
function main(input) {
    const X = bigInt(input.replace("\n", ""));
    let cur = bigInt(100);
    let ans = 0;
    while (cur < X) {
        ans++;
        cur = cur.add(cur.divide(100));
    }
    console.log(ans);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));